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<!DOCTYPE html> <html lang="en" class="grade-c"> <head> <title>The AiiDA-KKR plugin and its application to high-throughput impurity embedding into a topological insulator | npj Computational Materials</title> <link rel="alternate" type="application/rss+xml" href="https://www.nature.com/npjcompumats.rss"/> <link rel="preconnect" href="https://cmp.nature.com" crossorigin> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width,initial-scale=1.0,maximum-scale=5,user-scalable=yes"> <meta name="360-site-verification" content="5a2dc4ab3fcb9b0393241ffbbb490480" /> <script data-test="dataLayer"> window.dataLayer = 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data-test="article-title" data-article-title="">The AiiDA-KKR plugin and its application to high-throughput impurity embedding into a topological insulator</h1> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Philipp-R__mann-Aff1" data-author-popup="auth-Philipp-R__mann-Aff1" data-author-search="Rüßmann, Philipp" data-corresp-id="c1">Philipp Rüßmann<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><span class="u-js-hide"> <a class="js-orcid" href="http://orcid.org/0000-0002-6196-2700"><span class="u-visually-hidden">ORCID: </span>orcid.org/0000-0002-6196-2700</a></span><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Fabian-Bertoldo-Aff1" data-author-popup="auth-Fabian-Bertoldo-Aff1" data-author-search="Bertoldo, Fabian">Fabian Bertoldo</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> & </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Stefan-Bl_gel-Aff1" data-author-popup="auth-Stefan-Bl_gel-Aff1" data-author-search="Blügel, Stefan">Stefan Blügel</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul> <p class="c-article-info-details" data-container-section="info"> <a data-test="journal-link" href="/npjcompumats" data-track="click" data-track-action="journal homepage" data-track-category="article body" data-track-label="link"><i data-test="journal-title">npj Computational Materials</i></a> <b data-test="journal-volume"><span class="u-visually-hidden">volume</span> 7</b>, Article number: <span data-test="article-number">13</span> (<span data-test="article-publication-year">2021</span>) <a href="#citeas" class="c-article-info-details__cite-as u-hide-print" data-track="click" data-track-action="cite this article" data-track-label="link">Cite this article</a> </p> <div class="c-article-metrics-bar__wrapper u-clear-both"> <ul class="c-article-metrics-bar u-list-reset"> <li class=" c-article-metrics-bar__item" data-test="access-count"> <p class="c-article-metrics-bar__count">2126 <span class="c-article-metrics-bar__label">Accesses</span></p> </li> <li class="c-article-metrics-bar__item" data-test="altmetric-score"> <p class="c-article-metrics-bar__count">2 <span class="c-article-metrics-bar__label">Altmetric</span></p> </li> <li class="c-article-metrics-bar__item"> <p class="c-article-metrics-bar__details"><a href="/articles/s41524-020-00482-5/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Metrics <span class="u-visually-hidden">details</span></a></p> </li> </ul> </div> </header> <div class="u-js-hide" data-component="article-subject-links"> <h3 class="c-article__sub-heading">Subjects</h3> <ul class="c-article-subject-list"> <li class="c-article-subject-list__subject"><a href="/subjects/electronic-structure" data-track="click" data-track-action="view subject" data-track-label="link">Electronic structure</a></li><li class="c-article-subject-list__subject"><a href="/subjects/surfaces-interfaces-and-thin-films" data-track="click" data-track-action="view subject" data-track-label="link">Surfaces, interfaces and thin films</a></li><li class="c-article-subject-list__subject"><a href="/subjects/topological-insulators" data-track="click" data-track-action="view subject" data-track-label="link">Topological insulators</a></li> </ul> </div> </div> <div class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>The ever increasing availability of supercomputing resources led computer-based materials science into a new era of high-throughput calculations. Recently, Pizzi et al. introduced the AiiDA framework that provides a way to automate calculations while allowing to store the full provenance of complex workflows in a database. We present the development of the AiiDA-KKR plugin that allows to perform a large number of ab initio impurity embedding calculations based on the relativistic full-potential Korringa-Kohn-Rostoker Green function method. The capabilities of the AiiDA-KKR plugin are demonstrated with the calculation of several thousand impurities embedded into the prototypical topological insulator Sb<sub>2</sub>Te<sub>3</sub>. The results are collected in the JuDiT database which we use to investigate chemical trends as well as Fermi level and layer dependence of physical properties of impurities. This includes the study of spin moments, the impurity’s tendency to form in-gap states or its effect on the charge doping of the host-crystal. These properties depend on the detailed electronic structure of the impurity embedded into the host crystal which highlights the need for ab initio calculations in order to get accurate predictions.</p></div></div></section> <noscript> </noscript> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41699-023-00380-6/MediaObjects/41699_2023_380_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41699-023-00380-6?fromPaywallRec=false" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1038/s41699-023-00380-6">Absorption versus adsorption: high-throughput computation of impurities in 2D materials </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">01 April 2023</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41524-022-00730-w/MediaObjects/41524_2022_730_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41524-022-00730-w?fromPaywallRec=false" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1038/s41524-022-00730-w">Quantum point defects in 2D materials - the QPOD database </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">04 April 2022</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41578-021-00380-2/MediaObjects/41578_2021_380_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41578-021-00380-2?fromPaywallRec=false" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1038/s41578-021-00380-2">Topological materials discovery from crystal symmetry </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__date">01 November 2021</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1732323929, embedded_user: 'null' } }); </script> <div class="main-content"> <section data-title="Introduction"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1">Introduction</h2><div class="c-article-section__content" id="Sec1-content"><p>In recent years computer-driven materials design has become increasingly important in the field of materials science. The ever increasing availability of supercomputing resources opened up new possibilities towards data-driven condensed matter research. Apart from large collections of crystal structure information<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Villars, P., Cenzual, K., Gladyshevskii, R. & Iwata, S. PAULING FILE - towards a holistic view. Chem. Met. Alloys 11, 43–76 (2018)." href="#ref-CR1" id="ref-link-section-d112338150e368">1</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Hellenbrandt, M. The inorganic crystal structure database (ICSD)-present and future. Crystallography Rev. 10, 17–22 (2014)." href="#ref-CR2" id="ref-link-section-d112338150e368_1">2</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Grazulis, S. et al. Crystallography Open Database - an open-access collection ofcrystal structures. J. Appl. Cryst. 42, 726–729 (2009)." href="#ref-CR3" id="ref-link-section-d112338150e368_2">3</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="Draxl, C. & Scheffler, M. NOMAD: The FAIR concept for big data-driven materials science. MRS Bulletin 43, 676–682 (2018)." href="/articles/s41524-020-00482-5#ref-CR4" id="ref-link-section-d112338150e371">4</a></sup>, fully integrated frameworks of tools and databases have arisen that allow for high-throughput investigations using a huge amount of, mainly, density-functional-theory-based calculations<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Larsen, A. H. et al. The atomic simulation environment-A python library for working with atoms. J. Phys.: Condens. Matter 29, 273002 (2017)." href="#ref-CR5" id="ref-link-section-d112338150e375">5</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Curtarolo, S. et al. The high-throughput highway to computational materials design. Nature Mater. 12, 191–201 (2013)." href="#ref-CR6" id="ref-link-section-d112338150e375_1">6</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Jain, A. et al. Commentary: the Materials Project: a materials genome approach to accelerating materials innovation. APL Materials 1, 011002 (2013)." href="#ref-CR7" id="ref-link-section-d112338150e375_2">7</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. Comp. Mat. Sci. 111, 218 (2016)." href="/articles/s41524-020-00482-5#ref-CR8" id="ref-link-section-d112338150e378">8</a></sup>. Here, we present the AiiDA-KKR plugin<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="The AiiDA-KKR developers. The AiiDA-KKR plugin for the JuKKR codes. https://github.com/JuDFTteam/aiida-kkr ; https://doi.org/10.5281/zenodo.3628251 (2020)." href="/articles/s41524-020-00482-5#ref-CR9" id="ref-link-section-d112338150e382">9</a></sup> which connects our full-potential relativistic Korringa-Kohn-Rostoker Green function (KKR) method<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="The JuKKR developers. The Jülich KKR Codes. https://jukkr.fz-juelich.de (2020)." href="/articles/s41524-020-00482-5#ref-CR10" id="ref-link-section-d112338150e386">10</a></sup> to the AiiDA (Automated Interactive Infrastructure and Database for Computational Science) framework<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. Comp. Mat. Sci. 111, 218 (2016)." href="/articles/s41524-020-00482-5#ref-CR8" id="ref-link-section-d112338150e390">8</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 11" title="The AiiDA developers. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. http://www.aiida.net ." href="/articles/s41524-020-00482-5#ref-CR11" id="ref-link-section-d112338150e393">11</a></sup>.</p><p>The AiiDA infrastructure implements the FAIR principle<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 12" title="Wilkinson, M. D. et al. The FAIR Guiding Principles for scientific data management and stewardship. Sci Data 3, 160018 (2016)." href="/articles/s41524-020-00482-5#ref-CR12" id="ref-link-section-d112338150e400">12</a></sup> of findable, accessible, interoperable and reusable data sharing which provides a flexible plugin-based python environment. Through a common interface, different density-functional theory codes<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="The AiiDA plugin registry. https://aiidateam.github.io/aiida-registry/ ." href="/articles/s41524-020-00482-5#ref-CR13" id="ref-link-section-d112338150e404">13</a></sup> can even be used in combination to exploit the strengths of different implementations and realise multi-code workflows within the same framework. The KKR method is an all-electron implementation of density functional theory that allows accurate electronic structure calculations<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 14" title="Ebert, H., Ködderitzsch, D. & Minár, J. Calculating condensed matter properties using the KKR-Green’s function method-recent developments and applications. Rep. Prog. Phys. 74, 096501 (2011)." href="/articles/s41524-020-00482-5#ref-CR14" id="ref-link-section-d112338150e408">14</a></sup>, the extraction of magnetic response functions<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 15" title="Liechtenstein, A., Katsnelson, M., Antropov, V. & Gubanov, V. Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys. J. Magn. Magn. Mater. 67, 65 (1987)." href="/articles/s41524-020-00482-5#ref-CR15" id="ref-link-section-d112338150e412">15</a></sup> or gives access to transport properties<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Heers, S. Effect of spin-orbit scattering on transport properties of low-dimensional dilute alloys. Ph.D. thesis, RWTH Aachen University (2011)." href="#ref-CR16" id="ref-link-section-d112338150e416">16</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Long, N. H. et al. Spin relaxation and spin Hall transport in 5d transition-metal ultrathin film. Phys. Rev. B 90, 064406 (2014)." href="#ref-CR17" id="ref-link-section-d112338150e416_1">17</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Zimmermann, B. et al. Fermi surfaces, spin-mixing parameter, and colossal anisotropy of spin relaxation in transition metals from ab initio theory. Phys. Rev. B 93, 144403 (2016)." href="/articles/s41524-020-00482-5#ref-CR18" id="ref-link-section-d112338150e419">18</a></sup>. One of the advantages of the Green function formulation of the KKR method, which we focus on in this work, is the efficient treatment of defective systems (i.e., systems that contain defects and impurities) which can be very expensive to treat with wavefunction-based methods that often require very large supercells for this task. The AiiDA-KKR plugin is used to perform a large number of impurity embedding calculations into the prototypical topological insulator Sb<sub>2</sub>Te<sub>3</sub>.</p><p>Topological insulators (TIs) have been the center of attention in solid state research since their extraordinary physical properties, that lead to topologically protected surface states, have been discovered<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010)." href="/articles/s41524-020-00482-5#ref-CR19" id="ref-link-section-d112338150e431">19</a></sup>. In the past decade the field around topological materials has evolved steadily and now aims at functionalizing TI materials by interfacing them with other states of matter. For instance, realizing the quantum anomalous Hall (QAH)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="Yu, R. et al. Quantized anomalous hall effect in magnetic topological insulators. Science 329, 61–64 (2010)." href="/articles/s41524-020-00482-5#ref-CR20" id="ref-link-section-d112338150e435">20</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="Cui-Zu, C. et al. Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340, 6129 (2013)." href="/articles/s41524-020-00482-5#ref-CR21" id="ref-link-section-d112338150e438">21</a></sup> insulator state or Majorana zero modes<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="SankarDas, S., Freedman, M. & Nayak, C. Majorana zero modes and topological quantum computation. npj Quantum Inf 1, 15001 (2015)." href="/articles/s41524-020-00482-5#ref-CR22" id="ref-link-section-d112338150e442">22</a></sup>, that might lead to topological qubits, is pursued. The former requires to combine the topological band structures of TIs with magnetism while the latter needs interfacing topological materials with superconductors. Controlling the interface and understanding the effect defects and imperfections have remains a major challenge in this field to this day.</p><p>Apart from the development of the AiiDA-KKR plugin, the outcome of this study is the JuDiT database (Jülich Database of impurities embedded into a Topological insulator) of physical properties of impurities embedded into the surface of Sb<sub>2</sub>Te<sub>3</sub>. We study their tendency for charge doping (i.e., to introduce <i>p</i>- or <i>n</i>-doping), their impurity magnetic moments and their density of states (DOS). This collection of impurity properties allows to uncover chemical trends and can help to optimize the next generation of TI-based materials in the future. In particular, we investigate the layer and Fermi level dependence of the spin moment and find that Mo<sub>Sb</sub> defects show a high spin moment while introducing only a small charge doping, which is more than 5 times smaller than for magnetic 3<i>d</i> impurities. Furthermore, we find the Mo defect to be a good candidate for future applications since no impurity resonance appears in the bulk band gap region. An impurity resonance would otherwise lead to higher scattering rates of topological surface state electrons off this defect<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Rüßmann, P., Mavropoulos, P. & Blügel, S. Lifetime and surface-to-bulk scattering off vacancies of the topological surface state in the three-dimensional strong topological insulators Bi2Te3 and Bi2Se3. Journal of Physics and Chemistry of Solids https://doi.org/10.1016/j.jpcs.2017.12.009 (2017)." href="/articles/s41524-020-00482-5#ref-CR23" id="ref-link-section-d112338150e465">23</a></sup> and a higher probability to produce impurity bands in the gap.</p><p>The paper is structured as follows. The theoretical setting of the impurity embedding problem within the KKR method can be found in the Methods section. In the Results section, First the AiiDA-KKR package is presented where the calculation and workflow plugins, that are implemented in AiiDA-KKR, are discussed. Afterwards the developments are showcased at the example of high-throughput impurity embedding into the topological insulator material Sb<sub>2</sub>Te<sub>3</sub>. Finally, the Discussions section concludes the paper with a summary.</p></div></div></section><section data-title="Results"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2">Results</h2><div class="c-article-section__content" id="Sec2-content"><h3 class="c-article__sub-heading" id="Sec3">The AiiDA-KKR plugin</h3><p>The AiiDA framework<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. Comp. Mat. Sci. 111, 218 (2016)." href="/articles/s41524-020-00482-5#ref-CR8" id="ref-link-section-d112338150e489">8</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 11" title="The AiiDA developers. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. http://www.aiida.net ." href="/articles/s41524-020-00482-5#ref-CR11" id="ref-link-section-d112338150e492">11</a></sup> is a python package that allows to provide a code agnostic interface for different ab initio codes which enables the automation of calculations. Simultaneously, inputs and outputs of complex sequences of calculations are automatically saved in a database<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 24" title="The PostgreSQL Global Development Group. PostgreSQL: The world’s most advanced open source database. http://www.postgresql.org (2020)." href="/articles/s41524-020-00482-5#ref-CR24" id="ref-link-section-d112338150e496">24</a></sup>. This ensures the reproducibility of all results due to the stored provenance, which consist of nodes with directed connections, in the database. AiiDA implements the ADES model<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. Comp. Mat. Sci. 111, 218 (2016)." href="/articles/s41524-020-00482-5#ref-CR8" id="ref-link-section-d112338150e500">8</a></sup> which provides a common layer of data structures that are used by the plugins of different codes<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="The AiiDA plugin registry. https://aiidateam.github.io/aiida-registry/ ." href="/articles/s41524-020-00482-5#ref-CR13" id="ref-link-section-d112338150e504">13</a></sup>. This enables workflows that use multiple codes, which allows interoperability and exploitation of the individual strengths of different implementations.</p><p>To enable high-throughput KKR calculations with AiiDA we developed the open source AiiDA-KKR python plugin<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="The AiiDA-KKR developers. The AiiDA-KKR plugin for the JuKKR codes. https://github.com/JuDFTteam/aiida-kkr ; https://doi.org/10.5281/zenodo.3628251 (2020)." href="/articles/s41524-020-00482-5#ref-CR9" id="ref-link-section-d112338150e511">9</a></sup> that provides a set of calculations and workflows (i.e., complex sequences of calculations) and some accompanying tools. A detailed and up-to-date description of the input and output structure of the individual calculations, workflows and tools of AiiDA-KKR is included in its online documentation<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="The AiiDA-KKR developers. Documentation of the aiida-kkr plugin. https://aiida-kkr.readthedocs.io (2020)." href="/articles/s41524-020-00482-5#ref-CR25" id="ref-link-section-d112338150e515">25</a></sup> where additionally examples for the usage of the plugin are given. In the following only a brief overview of the features implemented in the AiiDA-KKR plugin is given.</p><p>Each calculation plugin comes with the functionality to create code-specific input files from AiiDA objects (e.g., <i>StructureData</i> objects that contain the structural information of a system) and a parser that is able to parse the retrieved output files. The conversion of AiiDA <i>Dict</i> objects to the input file needed by the JuKKR code is facilitated with a python class called <i>kkrparams</i><sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="The Masci-tools developers. Tools, utility, parsers useful in daily material science work. https://github.com/judftteam/aiida-kkr (2020)." href="/articles/s41524-020-00482-5#ref-CR26" id="ref-link-section-d112338150e530">26</a></sup> that also contains methods to verify the consistency of input parameter and write the input file. This class also knows about KKR-specific features like dealing with alloys within the coherent potential approximation<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 14" title="Ebert, H., Ködderitzsch, D. & Minár, J. Calculating condensed matter properties using the KKR-Green’s function method-recent developments and applications. Rep. Prog. Phys. 74, 096501 (2011)." href="/articles/s41524-020-00482-5#ref-CR14" id="ref-link-section-d112338150e534">14</a></sup>. Running a KKR calculation through AiiDA creates an acyclic directed graph in the database which is shown schematically for a <i>KkrCalculatio</i>n in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig1">1</a>(a). It can be seen that a calculation requires a few input nodes (input parameter <i>Dict</i> node, a <i>Code</i> node, and a <i>ParentCalculation</i> node), which are all AiiDA objects stored in the AiiDA database. The output files are retrieved once the calculation finished and parsed to extract output parameters, that are then stored as a <i>Dict</i> node in the database. It it worthwhile noting that the AiiDA daemon takes care of automatically storing the resulting nodes with their directed connections to the AiiDA database. This eventually results in a complex graph as it is shown schematically in (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig1">1</a>b, c) for a complete impurity-embedding sequence including all steps outlined in the Methods section. The full provenance of a complex procedure of calculations is stored in the database which allows to reproduce all inputs and the intermediate steps that have been performed to arrive at the final result. In the following the different calculations provided in the AiiDA-KKR plugin<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="The AiiDA-KKR developers. The AiiDA-KKR plugin for the JuKKR codes. https://github.com/JuDFTteam/aiida-kkr ; https://doi.org/10.5281/zenodo.3628251 (2020)." href="/articles/s41524-020-00482-5#ref-CR9" id="ref-link-section-d112338150e561">9</a></sup> are briefly discussed.</p><ul class="u-list-style-bullet"> <li> <p>The <i>VoronoiCalculation</i> plugin allows to use the <i>voronoi</i> code of the JuKKR package<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="The JuKKR developers. The Jülich KKR Codes. https://jukkr.fz-juelich.de (2020)." href="/articles/s41524-020-00482-5#ref-CR10" id="ref-link-section-d112338150e577">10</a></sup> which constructs the shape functions<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="Stefanou, N., Akai, H. & Zeller, R. An efficient numerical method to calculate shape truncation functions for Wigner-Seitz atomic polyhedra. Comput. Phys. Commun. 60, 231 (1990)." href="/articles/s41524-020-00482-5#ref-CR27" id="ref-link-section-d112338150e581">27</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="Stefanou, N. & Zeller, R. Calculation of shape-truncation functions for Voronoi polyhedra. J. Phys.: Cond. Matter 3, 7599 (1991)." href="/articles/s41524-020-00482-5#ref-CR28" id="ref-link-section-d112338150e584">28</a></sup> needed for the full-potential treatment and generates starting potentials. The graph of a <i>VoronoiCalculation</i> looks similar to the one shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig1">1</a>(a) except that the <i>ParentCalculation</i> input node is replaced by an AiiDA <i>StructureData</i> node that contains all structural information on the crystal (e.g., lattice constant, atom positions and kinds)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 11" title="The AiiDA developers. AiiDA: Automated Interactive Infrastructure and Database for Computational Science. http://www.aiida.net ." href="/articles/s41524-020-00482-5#ref-CR11" id="ref-link-section-d112338150e601">11</a></sup>.</p> </li> <li> <p>The <i>KkrCalculation</i> plugin provides an interface to the <i>KKRhost</i> code of JuKKR<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="The JuKKR developers. The Jülich KKR Codes. https://jukkr.fz-juelich.de (2020)." href="/articles/s41524-020-00482-5#ref-CR10" id="ref-link-section-d112338150e617">10</a></sup> which allows to perform self-consistency (scf), density of states (DOS), bandstructure and additional postprocessing calculations (e.g., calculation of Heisenberg exchange interaction parameters<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 15" title="Liechtenstein, A., Katsnelson, M., Antropov, V. & Gubanov, V. Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys. J. Magn. Magn. Mater. 67, 65 (1987)." href="/articles/s41524-020-00482-5#ref-CR15" id="ref-link-section-d112338150e621">15</a></sup>).</p> </li> <li> <p>The <i>KkrimpCalculation</i> plugin connects AiiDA to the <i>KKRimp</i> code of the JuKKR package that solves the Dyson equation for impurity embedding (Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41524-020-00482-5#Equ3">3</a>)). This calculation needs in addition to the usual inputs (input parameter (<i>Dict</i>) or <i>ParentCalculation</i> node) the host Green function in the impurity cluster region (<i>G</i><sup>host</sup>) which is written out with a special post-processing run-mode of the <i>KKRhost</i> program using a <i>KkrCalculation</i>. The <i>KkrimpCalculation</i> can then be used to perform electronic structure calculations for the impurity problem.</p> </li> </ul><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1" data-title="Structure of the AiiDA-KKR plugin."><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 1: Structure of the AiiDA-KKR plugin.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/1" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig1_HTML.png?as=webp"><img aria-describedby="Fig1" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig1_HTML.png" alt="figure 1" loading="lazy" width="685" height="274"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-1-desc"><p><b>a</b> Database structure of a typical KKR calculation performed with the AiiDA-KKR plugin. The node types and typical contents of the nodes are indicated and the arrows between nodes indicate the acyclicity of the graph. <b>b</b> Dependencies between the outputs and inputs of different calculations supported by the AiiDA-KKR plugin. <b>c</b> Simplified view of a chain of calculations with an indication which parts are automated by different nested workflows of AiiDA-KKR.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/1" data-track-dest="link:Figure1 Full size image" aria-label="Full size image figure 1" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>In addition to the calculation plugins, the AiiDA-KKR package provides some workflows that automate complex sequences of <i>voronoi</i>, <i>KKRhost</i> and <i>KKRimp</i> calculations. The workflows contained in AiiDA-KKR have been developed in a modular way and build upon each other. This is illustrated in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig1">1</a>(c) where the relation of the <i>kkr_imp_wc</i> and <i>kkr_imp_sub_wc</i> workflows is shown. Internally these are AiiDA <i>WorkChains</i> which is indicated by the <i>_wc</i> ending in the names of the workflows. For an in-depth discussion of the input and output structure and their usage we refer to the online documentation<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="The AiiDA-KKR developers. Documentation of the aiida-kkr plugin. https://aiida-kkr.readthedocs.io (2020)." href="/articles/s41524-020-00482-5#ref-CR25" id="ref-link-section-d112338150e718">25</a></sup>. Here we restrict our discussion to a short overview of the workflows of AiiDA-KKR.</p><ul class="u-list-style-bullet"> <li> <p>The <i>kkr_dos_wc</i> workflow conveniently wraps around a <i>KkrCalculation</i> and provides the necessary inputs to perform a DOS calculation. Additionally the output is parsed and the output DOS data is stored as an array in the database which allows easy access and plotting of the output DOS.</p> </li> <li> <p>The <i>voro_start_wc</i> workflow wraps the <i>VoronoiCalculation</i> and performs some additional verification of input structure and KKR-specific parameters in order to make sure the chosen starting setting is reasonable. One of the checks performed automatically within voro_start_wc makes use of the <i>kkr_dos_wc</i> workflow.</p> </li> <li> <p>The <i>kkr_scf_wc</i> workflow builds upon the <i>voro_start_wc</i> workflow and a sophisticated series of <i>KkrCalculations</i> which is intended to reach convergence of a given host system reliably. This makes sure the starting setup is reasonable before the potential is pre-converged until finally convergence with higher accuracy settings is pursued.</p> </li> <li> <p>The <i>gf_writeout_wc</i> workflow takes care of setting the necessary options for a <i>KkrCalculation</i> in order to write out <i>G</i><sup>host</sup> in preparation of the impurity embedding step. For a given impurity position and screening cluster size the host Green function can be reused for several impurities that respect this embedding geometry.</p> </li> <li> <p>The <i>kkr_imp_sub_wc</i> workflow performs the self consistency cycle of <i>KKRimp</i> calculations similar to the logic implemented in the <i>kkr_scf_wc</i> workflow. It includes features that deal with possible convergence problems automatically.</p> </li> <li> <p>The <i>kkr_imp_wc</i> workflow combines the <i>voro_start_wc</i>, <i>gf_writeout_wc</i> and <i>kkr_imp_sub_wc</i> steps for the impurity problem. This allows to conveniently start with a converged host calculation and the information on the impurity (e.g., its position in the host crystal, the size of the screening cluster) which defines the problem given by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41524-020-00482-5#Equ3">3</a>) completely.</p> </li> <li> <p>The <i>kkr_imp_dos_wc</i> workflow gives an easier access to calculate the DOS of an impurity embedded into a host crystal.</p> </li> </ul><p>Apart from tools that are used internally within the calculation and workflow plugins (e.g., to prepare the real space screening cluster), the AiiDA-KKR plugin contains a plotting tool called <i>plot_kkr</i>. This tool takes a node identifier (the AiiDA node instance, its <i>pk</i> or <i>uuid</i>) or even a list of nodes and plots a standard, yet fully customisable, plot of the respective data. For example, a typical self-consistency workflow for an impurity calculation (<i>kkr_imp_wc</i> node) as input to <i>plot_kkr</i> will produce a plot of the convergence behavior with the scf iteration number or an instance of a <i>kkr_imp_dos_wc</i> workflow will produce the orbital-resolved plot of the total DOS in the impurity cluster. Examples of such plots are given in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig2">2</a>. The tool conveniently abstracts away the need to extract the relevant data from the nodes in the database and provides a straightforward way to create commonly used plots.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2" data-title="The plot_kkr tool of AiiDA-KKR."><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 2: The <i>plot_kkr</i> tool of AiiDA-KKR.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/2" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig2_HTML.png?as=webp"><img aria-describedby="Fig2" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig2_HTML.png" alt="figure 2" loading="lazy" width="685" height="338"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-2-desc"><p>Illustration of typical plots generated with the <i>plot_kkr</i> tool of AiiDA-KKR (left: convergence behavior of a <i>kkr_imp_wc</i> workflow, right: DOS output of a <i>kkr_imp_dos_wc</i> workflow).</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/2" data-track-dest="link:Figure2 Full size image" aria-label="Full size image figure 2" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h3 class="c-article__sub-heading" id="Sec4">Example usage of AiiDA-KKR: Ag defect embedded into bulk Cu</h3><p>To illustrate how AiiDA-KKR’s python interface facilitates complex density functional calculations we demonstrate the use of the top-level workflows <i>kkr_scf_wc</i> and <i>kkr_imp_wc</i> at the example of an Ag impurity embedded into bulk fcc Cu. Solving this problem requires setting up the starting potential, converging the bulk electronic structure, writing out the host’s Green function for the impurity embedding and finally performing the impurity embedding step as sketched in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig1">1</a>(b, c). The AiiDA-KKR plugin conveniently automates this complex series of tasks. The code snippet in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig3">3</a> illustrates how the self-consistent calculation for the Cu bulk can be submitted to the AiiDA daemon that takes care of orchestrating the necessary sequence of <i>VoronoiCalculation</i> and <i>KkrCalculations</i>.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3" data-title="Submission of a self-consistency workflow for bulk Cu."><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 3: Submission of a self-consistency workflow for bulk Cu.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/3" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig3_HTML.png?as=webp"><img aria-describedby="Fig3" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig3_HTML.png" alt="figure 3" loading="lazy" width="685" height="82"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-3-desc"><p>The crystal structure is specified with the structure input and basic KKR-specific parameters, that control the accuracy of the calculation, are set in the <i>calc_parameters</i> input node. Here <i>submit</i>, <i>Dict</i> and <i>Code</i> are basic AiiDA methods and classes.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/3" data-track-dest="link:Figure3 Full size image" aria-label="Full size image figure 3" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Once the calculation for bulk fcc Cu finishes, the impurity embedding step can be done. This is equally simple with AiiDA-KKR’s python interface as the code snippet in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig4">4</a> demonstrates.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4" data-title="Submission of the complete impurity embedding workflow."><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 4: Submission of the complete impurity embedding workflow.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/4" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig4_HTML.png?as=webp"><img aria-describedby="Fig4" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig4_HTML.png" alt="figure 4" loading="lazy" width="685" height="95"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-4-desc"><p>The impurity calculation starts from the converged calculation of the Cu bulk system (called <i>scf</i> in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig3">3</a>). The impurity is specified via its nuclear charge, the position in the host crystal and the radius of the impurity cluster via the <i>impurity_info</i> input node.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/4" data-track-dest="link:Figure4 Full size image" aria-label="Full size image figure 4" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>In this example we define the Ag impurity which replaces a Cu atom and include a screening cluster around the impurity of 4 Å which contains the first two shells of Cu neighbors. From the converged calculation we can investigate the impurity DOS which is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig5">5</a>. It can be seen that embedding an Ag atom in the Cu crystal locally changes the electronic structure around the defect. This becomes evident in the appearance of a peak in the nearest neighbor Cu DOS at the position in energy where the Ag atoms has a resonance its DOS (highlighted by the black arrow). This resonance disappears already in the second Cu neighbor which shows the localized character of the impurity state. In addition, the inset in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig5">5</a> visualizes the resulting database structure of such a series of calculations (bulk scf, impurity scf, impurity DOS) where each node in the graph is an entry in the AiiDA database. The number of nodes and their connections highlight the complexity of the impurity embedding task that is conveniently taken over by the AiiDA-KKR plugin.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-5" data-title="Outcome of an impurity embedding calculation."><figure><figcaption><b id="Fig5" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 5: Outcome of an impurity embedding calculation.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/5" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig5_HTML.png?as=webp"><img aria-describedby="Fig5" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig5_HTML.png" alt="figure 5" loading="lazy" width="685" height="492"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-5-desc"><p>Density of states of an Ag<sub>Cu</sub> impurity and its surrounding Cu neighbors. The black arrow highlights the hybridization-induced states in the first Cu neighbor arising from the interaction with the <i>d</i>-resonance of the Ag defect. The inset (left) visualizes the database structure of the complete Ag<sub>Cu</sub> calculation which shows the complex relation between data nodes (structure input node, results <i>Dict</i> nodes etc.), logical nodes (e.g., different steps in <i>kkr_scf_wc</i> or <i>kkr_imp_wc</i> workflows) and calculations (<i>VoronoiCalculation</i>, <i>KkrCalculation</i> and <i>KkrimpCalculation</i>).</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/5" data-track-dest="link:Figure5 Full size image" aria-label="Full size image figure 5" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h3 class="c-article__sub-heading" id="Sec5">JuDiT – A database for impurities embedded into a TI</h3><p>We apply the AiiDA-KKR plugin to embed a large number of impurities into the topological insulator Sb<sub>2</sub>Te<sub>3</sub>. The resulting JuDiT database<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="Rüßmann, P., Bertoldo, F. & Blügel, S. The JuDiT database of impurities embedded into a Topological Insulator. Materials Cloud Archive 2020.0030/v1 https://doi.org/10.24435/materialscloud:nq-ht (2020)." href="/articles/s41524-020-00482-5#ref-CR29" id="ref-link-section-d112338150e1048">29</a></sup> comes with a webinterface<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Rüßmann, P., Bertoldo, F. & Blügel, S. JuDiT Database Discover section. https://pgi-jcns.fz-juelich.de/judit (2020)." href="/articles/s41524-020-00482-5#ref-CR30" id="ref-link-section-d112338150e1052">30</a></sup> for convenient access to the included data. The following analysis shows some of the physical insights obtained through this study. Our data analysis does not aim at being comprehensive but is intended to showcase the usefulness of our application. A future data-driven study might give additional insights but is beyond the scope of this work.</p><p>For the JuDiT database we considered substitutional defects (denoted by <i>X</i><sub><i>Y</i></sub> for impurity <i>X</i> replacing host atom <i>Y</i>) in the first 3 quintuple layers (QL) of a 6 QL thick film of Sb<sub>2</sub>Te<sub>3</sub>. This allows to study the influence of the topological surface state, that is mainly located in the 1st QL, on impurity properties. The band structure and DOS of the clean host system are shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig6">6</a>. In order to take into consideration doping of the host material, we investigated three possible positions of the Fermi level (<i>E</i><sub><i>F</i></sub> located in the valence band (VB) and in the conduction band (CB), as well as <i>E</i><sub><i>F</i></sub> in the bulk band gap). The shifted positions of the Fermi level are highlighted in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig6">6</a> with red (<i>E</i><sub><i>F</i></sub> in VB) and green (<i>E</i><sub><i>F</i></sub> in CB) lines. For the impurity embedding we neglected structural relaxations of the atoms around the impurities but included the first 3-4 shells of neighbors (containing 21–27 atoms and empty cells in the impurity cluster) within a radius of 4.8 Å around the impurities. We used the exact description of the atomic cells<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="Stefanou, N., Akai, H. & Zeller, R. An efficient numerical method to calculate shape truncation functions for Wigner-Seitz atomic polyhedra. Comput. Phys. Commun. 60, 231 (1990)." href="/articles/s41524-020-00482-5#ref-CR27" id="ref-link-section-d112338150e1107">27</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="Stefanou, N. & Zeller, R. Calculation of shape-truncation functions for Voronoi polyhedra. J. Phys.: Cond. Matter 3, 7599 (1991)." href="/articles/s41524-020-00482-5#ref-CR28" id="ref-link-section-d112338150e1110">28</a></sup> and the local spin density approximation<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="Vosko, S. H., Wilk, L. & Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200 (1980)." href="/articles/s41524-020-00482-5#ref-CR31" id="ref-link-section-d112338150e1114">31</a></sup> (LSDA) for the exchange correlation functional. A cutoff for the angular expansion of <span class="mathjax-tex">${\ell }_{\max }=3$</span> was chosen and corrections for the truncation error using Lloyd’s formula have been applied<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="Zeller, R. An elementary derivation of Lloyd’s formula valid for full-potential multiple-scattering theory. J. Phys. Cond. Matt. 16, 6453 (2004)." href="/articles/s41524-020-00482-5#ref-CR32" id="ref-link-section-d112338150e1154">32</a></sup>. Relativistic corrections arising within the scalar-relativistic approximations as well as spin-orbit coupling have been taken into account fully self-consistently for both host and impurity calculations. This approach has been applied successfully in the past to study magnetic and non-magnetic defects in topological insulators where a good agreement between our theoretical predictions and different experimental observations was verified<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Rüßmann, P., Mavropoulos, P. & Blügel, S. Lifetime and surface-to-bulk scattering off vacancies of the topological surface state in the three-dimensional strong topological insulators Bi2Te3 and Bi2Se3. Journal of Physics and Chemistry of Solids https://doi.org/10.1016/j.jpcs.2017.12.009 (2017)." href="/articles/s41524-020-00482-5#ref-CR23" id="ref-link-section-d112338150e1158">23</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Sessi, P. et al. Superparamagnetism-induced mesoscopic electron focusing in topological insulators. Phys. Rev. B 94, 075137 (2016)." href="#ref-CR33" id="ref-link-section-d112338150e1161">33</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Rüßmann, P. et al. Towards microscopic control of the magnetic exchange coupling at the surface of a topological insulator. J. Phys. Mater. 1, 015002 (2018)." href="#ref-CR34" id="ref-link-section-d112338150e1161_1">34</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Peixoto, T. R. F. et al. Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators. npj Quantum Mater. 5, 87 (2020)." href="/articles/s41524-020-00482-5#ref-CR35" id="ref-link-section-d112338150e1164">35</a></sup>.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6" data-title="Electronic structure of Sb2Te3."><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 6: Electronic structure of Sb<sub>2</sub>Te<sub>3</sub>.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/6" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig6_HTML.png?as=webp"><img aria-describedby="Fig6" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig6_HTML.png" alt="figure 6" loading="lazy" width="685" height="233"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-6-desc"><p>Band structure in terms of the Bloch spectral function (<b>a</b>) and density of states (<b>b</b>) of the 6 quintuple-layer thick Sb<sub>2</sub>Te<sub>3</sub> host crystal. Indicated are the bulk band-gap region (light blue region) as well as the in the considered Fermi level shifts (red and green lines) that are used to simulate the effect of <i>p</i>- and <i>n</i>-doping in the topological insulator host material.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/6" data-track-dest="link:Figure6 Full size image" aria-label="Full size image figure 6" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>We start our analysis with an overview of the contents of the JuDiT database. In total more than 2100 impurities have been embedded self-consistently into the Sb<sub>2</sub>Te<sub>3</sub> host system. For each impurity we computed physical properties like the spin and orbital moments, the impurity’s DOS as well as the tendency to show impurity resonance in the region of the bulk band gap. Furthermore, we analyzed the charge doping introduced by the defect which we define as</p><div id="Equ1" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${{\Delta }}{n}^{{\rm{imp}}}=({n}^{{\rm{imp}}}-{Z}^{{\rm{imp}}})-({n}^{{\rm{host}}}-{Z}^{{\rm{host}}}),$$</span></div><div class="c-article-equation__number"> (1) </div></div><p>where <i>n</i><sup>imp</sup> (<i>n</i><sup>host</sup>) are the electron densities for the impurity (host) atom embedded into the surrounding host crystal integrated in the Voronoi cell of the atom. Here, <i>Z</i><sup>imp</sup> (<i>Z</i><sup>host</sup>) is the nuclear charge of the impurity (host) atom. The expression in brackets in the rhs of Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41524-020-00482-5#Equ1">1</a>) therefore contain the information how much charge is transferred to/from the impurity.</p><p>The results can conveniently be visualized with the JuDiT webinterface<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Rüßmann, P., Bertoldo, F. & Blügel, S. JuDiT Database Discover section. https://pgi-jcns.fz-juelich.de/judit (2020)." href="/articles/s41524-020-00482-5#ref-CR30" id="ref-link-section-d112338150e1364">30</a></sup>. The plots from Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig6">6</a> as well as the ones of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig7">7</a> have been created using the tools available there. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig7">7</a>(a) displays the, over the different impurity sites averaged, charge doping given in electrons per impurity. The observed chemical trends partly fit the behavior of the Pauling electronegativity<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 36" title="Lide, D. R. Table of electronegativity on the Pauling scale. CRC Handbook of Chemistry and Physics 90 (2010)." href="/articles/s41524-020-00482-5#ref-CR36" id="ref-link-section-d112338150e1377">36</a></sup>. This causal relation is highlighted by a Pearson correlation coefficient of 0.5 which is found between the induced charge density and the impurity’s electronegativity (see Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">2</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">3</a> for details). The details of the bonding mechanism are however more subtle and can be quantified using ab initio data. This reflects the intricate physics of the chemical bonding which was recently classified to be <i>metavalent</i> for the Sb<sub>2</sub>Te<sub>3</sub> class of materials<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 37" title="Yu, Y., Cagnoni, M., Cojocaru-Mirédin, O. & Wuttig, M. Chalcogenide thermoelectrics empowered by an unconventional bonding mechanism. Adv. Funct. Mater. 1904862 (2019)." href="/articles/s41524-020-00482-5#ref-CR37" id="ref-link-section-d112338150e1395">37</a></sup>.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-7" data-title="Impurity properties of defects in Sb2Te3."><figure><figcaption><b id="Fig7" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 7: Impurity properties of defects in Sb<sub>2</sub>Te<sub>3</sub>.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/7" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig7_HTML.png?as=webp"><img aria-describedby="Fig7" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig7_HTML.png" alt="figure 7" loading="lazy" width="685" height="954"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-7-desc"><p><b>a</b> Overview of the impurity-induced charge doping (averaged over all considered impurity configurations, given in electrons per impurity atom). <b>b</b> Impurity density of states for a Tc<sub>Sb</sub> defect showing a resonance arising in the bulk band gap region (blue shaded region). Positive and negative values correspond to minority and majority states. <b>c</b> Location of the Tc<sub>Sb</sub> impurity in the Sb<sub>2</sub>Te<sub>3</sub> host crystal. The full-colored spheres represent the atoms in the impurity cluster and the opaque atoms show the rest of the host crystal where Δ<i>V</i> = 0.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/7" data-track-dest="link:Figure7 Full size image" aria-label="Full size image figure 7" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Each impurity in JuDiT also has a detail page where the complete output dictionary of the converged calculation is given and from where its provenance can be browsed. It also features a plot of the impurity DOS which is shown exemplary in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig7">7</a>(b) for a Tc<sub>Sb</sub> impurity located in the fourth Sb layer from the surface. The position of the impurity in the Sb<sub>2</sub>Te<sub>3</sub> host crystal is visualized in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig7">7</a>(c). It can be seen that the <i>d</i>-states of the Tc atom are exchange- and crystal-field-split which results in a magnetic moment of the impurity and a resonance in the impurity DOS around the Fermi level consequently in the bulk band gap region (blue area in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig7">7</a>(b), see also Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig6">6</a>). This particular defect is therefore expected to lead to strong scattering of the topological surface state electrons<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Rüßmann, P., Mavropoulos, P. & Blügel, S. Lifetime and surface-to-bulk scattering off vacancies of the topological surface state in the three-dimensional strong topological insulators Bi2Te3 and Bi2Se3. Journal of Physics and Chemistry of Solids https://doi.org/10.1016/j.jpcs.2017.12.009 (2017)." href="/articles/s41524-020-00482-5#ref-CR23" id="ref-link-section-d112338150e1471">23</a></sup> which can induce significant back-scattering since the Tc defect is a resonant scatterer <i>and</i> is magnetic with a spin moment of 1.86 <i>μ</i><sub>B</sub>.</p><p>In order to quantify the gap-filling nature of all considered defects, we define the number of states introduced by the defect in the bulk band gap region as</p><div id="Equ2" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${n}_{{\rm{gap}}}^{{\rm{imp}}}={\int \nolimits_{{E}_{\min }}^{{E}_{\max }}}{\rm{d}}E\int _{{{{\Omega }}}_{{\rm{Imp}}}}{{\rm{d}}}^{3}r\ \rho ({\boldsymbol{r}};E),$$</span></div><div class="c-article-equation__number"> (2) </div></div><p>where <span class="mathjax-tex">${E}_{\min }$</span> and <span class="mathjax-tex">${E}_{\max }$</span> are the edges of the bulk band gap region (blue area in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig6">6</a>), Ω<sub>imp</sub> is the Voronoi cell around the impurity atom and <i>ρ</i>(<b><i>r</i></b>; <i>E</i>) denotes the charge density around the atom in the Voronoi cell. A high gap-filling value consequently signals that scattering off that particular impurity will be increased which could be detrimental to the desired transport properties of TI materials. This is especially the case if the impurity is magnetic and the <b><i>k</i></b> → −<b><i>k</i></b> backscattering channel reopens due to broken time reversal symmetry.</p><p>We now focus our attention to magnetic defects which are found for some transition metal impurities. These systems are interesting in the context of realizing a robust QAH phase. We start by investigating the layer and Fermi level dependence of the spin moment of 3<i>d</i> transition metal impurities shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig8">8</a>(a). We see a gradual increase of the magnetic moment when going from V over Cr up to Mn dopants (blue orange and green symbols, respectively) before a subsequent decrease with Fe and Co impurities (red, violet) is observed. This behavior is expected from Hund’s rule and reflects the, from V to Co, increasing filling of the <i>d</i>-shell (see also Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">1</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">1</a>).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-8" data-title="Charge doping and magnetic properties of defects in Sb2Te3."><figure><figcaption><b id="Fig8" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 8: Charge doping and magnetic properties of defects in Sb<sub>2</sub>Te<sub>3</sub>.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/8" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig8_HTML.png?as=webp"><img aria-describedby="Fig8" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_Fig8_HTML.png" alt="figure 8" loading="lazy" width="685" height="367"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-8-desc"><p><b>a</b> Layer and Fermi level dependence (<i>E</i><sub><i>F</i></sub> − 200 meV: <span class="stix">△</span>, <i>E</i><sub><i>F</i></sub>: <span class="stix">○</span>, <i>E</i><sub><i>F</i></sub> + 200 meV: □) of the spin moment of some 3<i>d</i>-impurities. The blue dotted lines serve as guides to the eye to highlight the difference in the spin-moment for Te and Sb layers. <b>b</b> Charge doping (in units of added electrons per impurity) vs. impurity atomic charge of all considered impurities. The color of the data points in (<b>b</b>) refers to the magnitude of the spin moment (blue: non magnetic to yellow: 4.4 <i>μ</i><sub><i>B</i></sub>). The arrows highlight magnetic 3<i>d</i> and 4<i>d</i> impurities which differ in their induced charge doping to the host crystal. The plot in (<b>b</b>) was generated using the JuDiT web interface<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Rüßmann, P., Bertoldo, F. & Blügel, S. JuDiT Database Discover section. https://pgi-jcns.fz-juelich.de/judit (2020)." href="/articles/s41524-020-00482-5#ref-CR30" id="ref-link-section-d112338150e1799">30</a></sup> that accompanies the publication and can be used to visualize and export the result for future studies.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41524-020-00482-5/figures/8" data-track-dest="link:Figure8 Full size image" aria-label="Full size image figure 8" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>The details of the impurity’s electronic structure are largely determined by two factors: (i) the atomic nature of the impurity atom determining its number of electrons in the atomic configuration and (ii) the interaction with the surrounding atoms of the host crystal that affect the hybridization of the atomic states of the impurity with the host’s band structure. This effect is seen in the layer dependence of the size of the spin-moment which is highlighted for V<sub>Sb</sub> and V<sub>Te</sub> defects with the blue dashed lines in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig8">8</a>(a). We observe a higher spin-moment for V<sub>Te</sub> compared to V<sub>Sb</sub> which can be attributed to a larger charge transfer to the impurity in the Sb substitutional site compared to the Te substitutional site. The larger charge transfer to the impurity results in a higher filling of the V <i>d</i>-shell and therefore a higher spin moment which can also be seen for the Cr impurity. The same mechanism leads to a decrease in the spin moment that is found for Co<sub>Sb</sub> defects compared to Co<sub>Te</sub>.</p><p>Investigating the dependence of the impurity spin moment on the Fermi level (different symbols in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig8">8</a>(a)) reveals that the details of the hybridization with the electronic band structure of the host material can be controlled via the position of the Fermi level in the host material. A shift in the host’s Fermi level can experimentally be achieved by appropriate doping with Bi<sub>Sb</sub> impurities<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 38" title="Kellner, J. et al. Tuning the Dirac point to the Fermi level in the ternary topological insulator (Bi1−xSbx)2Te3. Appl. Phys. Lett. 107, 251603 (2015)." href="/articles/s41524-020-00482-5#ref-CR38" id="ref-link-section-d112338150e1841">38</a></sup>. This change in the impurity moment has been seen previously both theoretical<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 34" title="Rüßmann, P. et al. Towards microscopic control of the magnetic exchange coupling at the surface of a topological insulator. J. Phys. Mater. 1, 015002 (2018)." href="/articles/s41524-020-00482-5#ref-CR34" id="ref-link-section-d112338150e1845">34</a></sup> as well as experimental<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Peixoto, T. R. F. et al. Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators. npj Quantum Mater. 5, 87 (2020)." href="/articles/s41524-020-00482-5#ref-CR35" id="ref-link-section-d112338150e1849">35</a></sup> and can be attributed to the competition between the impurity seeking charge neutrality and the strong change in the hybridization with the host’s electronic structure with varying position of the Fermi level due to the presence of the bulk band gap in TI materials. This leads, for instance, to decreasing (increasing) spin moments for V<sub>Sb</sub> (V<sub>Te</sub>) with increasing position of the Fermi level.</p><p>Overall we observe that for <i>V</i> impurities the spread in the spin moment with the impurity’s surrounding (i.e., its layer dependence) is twice as large as with varying Fermi level. On the contrary, for Mn defects the change in the spin moment in different layers and with varying Fermi level is always rather small. This results from the half-filling of the Mn <i>d</i> orbital that make the spin moment relatively insensitive to small changes in the hybridization with the host’s electronic structure. Nevertheless, the magnetic interactions among multiple magnetic impurity atoms can, even at small changes in the impurity hybridization, be strongly affected<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 34" title="Rüßmann, P. et al. Towards microscopic control of the magnetic exchange coupling at the surface of a topological insulator. J. Phys. Mater. 1, 015002 (2018)." href="/articles/s41524-020-00482-5#ref-CR34" id="ref-link-section-d112338150e1867">34</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Peixoto, T. R. F. et al. Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators. npj Quantum Mater. 5, 87 (2020)." href="/articles/s41524-020-00482-5#ref-CR35" id="ref-link-section-d112338150e1870">35</a></sup>.</p><p>Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig8">8</a>(b) summarizes the charge doping Δ<i>n</i><sup>imp</sup> for all defects included in JuDiT. The zigzag behavior with the impurity’s core charge reflects the structure of the periodic table with its isoelectronic groups. This is verified by a Pearson correlation coefficient of 0.68 between the impurity’s group index and the induced charge doping (see Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">4</a> for details). Each data point in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41524-020-00482-5#Fig8">8</a>(b) is colored by the impurity’s spin moment which shows that the maximum of the spin-moment is found for Mn and Fe impurities (yellow points). It can however be seen that the charge doping introduced by these 3<i>d</i> defects is fairly large which reflects the significant difference in electronegativity compared to the Sb and Te host atoms<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 36" title="Lide, D. R. Table of electronegativity on the Pauling scale. CRC Handbook of Chemistry and Physics 90 (2010)." href="/articles/s41524-020-00482-5#ref-CR36" id="ref-link-section-d112338150e1895">36</a></sup>.</p><p>Applying magnetic doping to achieve a robust QAH phase needs to fulfill some boundary conditions in order to be feasible in experiments. In order to not tune the Fermi level out of the bulk band gap by magnetic doping, the induced charge doping should be as small as possible. At the same time magnetism is the key ingredient which calls for a sizable spin moment of the impurity. Furthermore, the magnetic impurity should not show a high DOS in the bulk band gap region to reduce the appearance of unwanted impurity bands with increasing magnetic doping. If we apply these conditions of a gap filling of <span class="mathjax-tex">${n}_{{\rm{gap}}}^{{\rm{imp}}}\, < \,0.02\ {\rm{e}}$</span>, a charge doping of Δ<i>n</i><sup>imp</sup> < 0.1 e and a spin-moment of <i>m</i><sub><i>s</i></sub> > 1.5 μ<sub>B</sub> we find that Mo<sub>Sb</sub> defects meet all these criteria. Compared to the Te substitutional site, which also shows a small charge doping and high spin moment, the Sb substitution have a gap filling which is an order of magnitude smaller and could therefore be desirable. To be able to use Mo-dopants for the realization of the QAH state the magnetic exchange coupling between Mo atoms needs to be investigated further in the future. This is, however, beyond the scope of this work. The study of the exchange interactions will be especially interesting since Mo-doping of Bi<sub>2</sub>Se<sub>3</sub> showed signatures of antiferromagnetic coupling<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 39" title="Deng, B., Liu, F. & Zhu, J. Absence of quantum anomalous Hall state in 4d transition-metal-doped Bi2Se3: An ab initio study. Phys. Rev. B 96, 174404 (2017)." href="/articles/s41524-020-00482-5#ref-CR39" id="ref-link-section-d112338150e1973">39</a></sup> which could be possibly overcome by appropriate band structure and defect engineering as it was seen for Mn and Co doping of Bi<sub>2</sub>Te<sub>3</sub><sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 34" title="Rüßmann, P. et al. Towards microscopic control of the magnetic exchange coupling at the surface of a topological insulator. J. Phys. Mater. 1, 015002 (2018)." href="/articles/s41524-020-00482-5#ref-CR34" id="ref-link-section-d112338150e1981">34</a></sup>. Here, additional codoping with other defects could open another way to design TI-based materials for future applications<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Kim, J., Jhi, S.-H., MacDonald, A. H. & Wu, R. Ordering mechanism and quantum anomalous Hall effect of magnetically doped topological insulators. Phys. Rev. B 96, 140410(R) (2017)." href="/articles/s41524-020-00482-5#ref-CR40" id="ref-link-section-d112338150e1985">40</a></sup>.</p><p>In the framework of density functional theory the effect of on-site Coulomb repulsion for localized <i>d</i> or <i>f</i> electrons can be included with the LDA+U method<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 41" title="Ebert, H., Perlov, A. & Mankovsky, S. Incorporation of the rotationally invariant LDA + U scheme into the SPR-KKR formalism: application to disordered alloys. Solid State Commun. 127, 443–446 (2003)." href="/articles/s41524-020-00482-5#ref-CR41" id="ref-link-section-d112338150e1998">41</a></sup>. We applied this scheme for 153 transition metal defects in the JuDiT database. For the parametrization of the correlations we used the U and J values calculated from the constrained random-phase approximation<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Sasioglu, E., Friedrich, C. & Blügel, S. Effective Coulomb interaction in transition metals from constrained random-phase approximation. Phys. Rev. B 83, 121101(R) (2011)." href="/articles/s41524-020-00482-5#ref-CR42" id="ref-link-section-d112338150e2002">42</a></sup>. The values for the LDA+U parametrization used in this work for the transition metal impurities are given in Supplementary Table <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">1</a>. Generally, including correlations within the LDA+U method increases the exchange splitting in magnetic impurities. This is seen, for example, in the comparison of the DOS of 3<i>d</i> transition metal defects with and without U-corrections (see Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">2</a>). Adding correlation effects also changes other physical properties which manifests in an increase in the median value of the spin moment by 36% (see Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">5</a>) for the LDA+U calculations compared to the previously discussed LDA results. An even stronger effect is seen on the orbital moment where we find a decrease of 58% in the median value for the subset of impurities where LDA+U calculations have been included. These results indicate that local correlations can strongly affect the outcome and should be considered when comparing calculations and experimental results.</p><p>In order to review the accuracy of our calculations and estimate possible shortcomings of our approach we attempt a comparison of physical properties contained in the JuDiT database to already published experimental and theoretical results. We focus on (i) the experimentally observed charge doping in Sb<sub>2</sub>Te<sub>3</sub> and (ii) magnetic properties reported mainly for V and Cr doped (Bi,Sb)<sub>2</sub>Te<sub>3</sub>.</p><p>In experiments, Sb<sub>2</sub>Te<sub>3</sub> is typically found to be <i>p</i>-doped which is associated to the abundance of intrinsic Sb<sub>Te</sub> anti site defects<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Lostak, P., Stary, Z., Horak, J. & Pancir, J. Substitutional defects in Sb2Te3 crystals. Phys. Stat. Sol. (a) 115, 87 (1989)." href="/articles/s41524-020-00482-5#ref-CR43" id="ref-link-section-d112338150e2042">43</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="Cava, R. J., Ji, H., Fuccillo, M. K., Gibson, Q. D. & Ho, Y. S. Crystal structure and chemistry of topological insulators. J. Mater. Chem. C 1, 3176 (2013)." href="/articles/s41524-020-00482-5#ref-CR44" id="ref-link-section-d112338150e2045">44</a></sup>. This trend is confirmed by results for the impurity induced charge doping in the JuDiT database which is found to be negative ( ≈ − 0.01 <i>e</i> per imp. for <i>p</i>-doped Sb<sub>2</sub>Te<sub>3</sub>). In addition, Te<sub>Sb</sub> defects show the same trend which is in line with the experimental observation that <i>n</i>-type doping is not realized in Sb<sub>2</sub>Te<sub>3</sub> even under Te rich growing conditions<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="Cava, R. J., Ji, H., Fuccillo, M. K., Gibson, Q. D. & Ho, Y. S. Crystal structure and chemistry of topological insulators. J. Mater. Chem. C 1, 3176 (2013)." href="/articles/s41524-020-00482-5#ref-CR44" id="ref-link-section-d112338150e2070">44</a></sup>. However, the size of the charge doping that results from our calculations is rather small which might indicate that in strongly doped materials collective effects can lead to a more pronounced effect. This can, for instance, result from the long-ranged Coulomb interaction among charged defects that leads to a shift in the Fermi level of the whole crystal<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 45" title="Van de Walle, C. G. & Neugebauer, J. First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys. 95, 3851 (2004)." href="/articles/s41524-020-00482-5#ref-CR45" id="ref-link-section-d112338150e2074">45</a></sup>.</p><p>In the literature doping of Sb<sub>2</sub>Te<sub>3</sub> is mostly studied in the context of possible realizations of the QAH effect with magnetic dopants. In Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/articles/s41524-020-00482-5#Tab1">1</a> we collected some experimental (e.g., from XMCD data) and theoretical (e.g., DFT supercell calculations) results for the spin moment of transition metal doped Sb<sub>2</sub>Te<sub>3</sub> compounds. We focus on the LDA results since most calculations in the literature do not report values including correlation effects.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-1"><figure><figcaption class="c-article-table__figcaption"><b id="Tab1" data-test="table-caption">Table 1 Spin moments in <i>μ</i><sub><i>B</i></sub> of 3<i>d</i> transition metal doped Sb<sub>2</sub>Te<sub>3</sub> compounds.</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/articles/s41524-020-00482-5/tables/1" aria-label="Full size table 1"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>We can see that there is a considerable spread in the reported values for the spin moment of different impurities. Taking this methodological variance into account we find a reasonable agreement with our data from the JuDiT database. We suspect that the slight overestimation of the spin moment for V and Cr is a result of the neglected structural relaxations around the defects. The appearance of a resonance in the impurity DOS around the Fermi level (see Supplementary Figs. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">1</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/articles/s41524-020-00482-5#MOESM1">2</a>) could be removed by structural relaxations. In the spirit of the Jahn-Teller effect this could change the <i>d</i>-filling of the impurity and consequently lead to smaller spin moments for V and Cr defects. A future study focusing on this effect might give more insights into the effect of structural relaxations. Some experiments<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Peixoto, T. R. F. et al. Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators. npj Quantum Mater. 5, 87 (2020)." href="/articles/s41524-020-00482-5#ref-CR35" id="ref-link-section-d112338150e2480">35</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 46" title="Peixoto, T. R. F. et al. Impurity states in the magnetic topological insulator V:(Bi,Sb)2Te3. Phys. Rev. B 94, 195140 (2016)." href="/articles/s41524-020-00482-5#ref-CR46" id="ref-link-section-d112338150e2483">46</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 47" title="Islam, M. F. et al. Systematics of electronic and magnetic properties in the transition metal doped Sb2Te3 quantum anomalous Hall platform. Phys. Rev. B 97, 155429 (2018)." href="/articles/s41524-020-00482-5#ref-CR47" id="ref-link-section-d112338150e2486">47</a></sup> additionally report on the measured impurity DOS for V and Cr defects from resonant photoemission spectroscopy or scanning tunneling spectroscopy. A comparison to our calculated impurity DOS spectra shows good agreement for defects at the substitutional Sb site which is in line with the reasonable agreement of the spin moment reported in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/articles/s41524-020-00482-5#Tab1">1</a>.</p></div></div></section><section data-title="Discussion"><div class="c-article-section" id="Sec6-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec6">Discussion</h2><div class="c-article-section__content" id="Sec6-content"><p>In conclusion, we have developed the AiiDA-KKR plugin which is an open source python package that connects the JuKKR code family to the AiiDA framework. This allows to perform Korringa-Kohn-Rostoker Green function calculations in an automated high-throughput manner. We concentrated on the ability to perform ab initio impurity embedding into the topological insulator Sb<sub>2</sub>Te<sub>3</sub>.</p><p>We considered several thousand different impurities embedded into the different layers of the Sb<sub>2</sub>Te<sub>3</sub> host crystal. This procedure allowed us to study the layer and Fermi level dependence of physical properties of defects. Specifically, we studied the chemical trends in terms of the impurity’s charge doping, their tendency to create resonances in the bulk band gap and their magnetic properties. The results have been collected in the JuDiT database which is openly available and comes with online tools for data visualization and export. Throughout our analysis we have seen that the details of the electronic structure of an impurity embedded into a host crystal is very important. The hybridization of the impurity states with its surrounding plays a crucial role for its physical properties. This highlights the relevance and the need for our ab initio calculations which provide predictive power.</p><p>In the future the AiiDA-KKR plugin in general and the resulting data of this study in particular can be used in broader high-throughput studies for quantum materials. The capabilities of AiiDA-KKR could be extended to further include the automated calculation of scattering<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 16" title="Heers, S. Effect of spin-orbit scattering on transport properties of low-dimensional dilute alloys. Ph.D. thesis, RWTH Aachen University (2011)." href="/articles/s41524-020-00482-5#ref-CR16" id="ref-link-section-d112338150e2516">16</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="Long, N. H. et al. Spin relaxation and spin Hall transport in 5d transition-metal ultrathin film. Phys. Rev. B 90, 064406 (2014)." href="/articles/s41524-020-00482-5#ref-CR17" id="ref-link-section-d112338150e2519">17</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="Rüßmann, P., Mavropoulos, P. & Blügel, S. Ab-initio theory of fourier-transformed quasiparticle interference maps and application to the topological insulator Bi2Te3. phys. stat. sol. (b), in press, https://doi.org/10.1002/pssb.202000031 (2020)." href="/articles/s41524-020-00482-5#ref-CR48" id="ref-link-section-d112338150e2522">48</a></sup> and transport properties<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Zimmermann, B. et al. Fermi surfaces, spin-mixing parameter, and colossal anisotropy of spin relaxation in transition metals from ab initio theory. Phys. Rev. B 93, 144403 (2016)." href="/articles/s41524-020-00482-5#ref-CR18" id="ref-link-section-d112338150e2526">18</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 49" title="Kosma, A., Rüßmann, P., Blügel, S. & Mavropoulos, P. Strong Spin-Orbit Torque effect on magnetic defects due to topological surface state electrons in Bi2Te3. Phys. Rev. B 102, 144424 (2020)." href="/articles/s41524-020-00482-5#ref-CR49" id="ref-link-section-d112338150e2529">49</a></sup> or to investigate magnetic exchange interactions<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 15" title="Liechtenstein, A., Katsnelson, M., Antropov, V. & Gubanov, V. Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys. J. Magn. Magn. Mater. 67, 65 (1987)." href="/articles/s41524-020-00482-5#ref-CR15" id="ref-link-section-d112338150e2533">15</a></sup>. Especially the vast space of combinations codoping with other impurities introduces will be of interest in order to find ways to tune physical properties and engineer the behavior of TI-based materials.</p></div></div></section><section data-title="METHODS"><div class="c-article-section" id="Sec7-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec7">METHODS</h2><div class="c-article-section__content" id="Sec7-content"><h3 class="c-article__sub-heading" id="Sec8">Ab initio impurity embedding</h3><p>One of the advantages that arises from the Green function formulation of the KKR method lies in its ability to include impurities efficiently into crystalline solids<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 14" title="Ebert, H., Ködderitzsch, D. & Minár, J. Calculating condensed matter properties using the KKR-Green’s function method-recent developments and applications. Rep. Prog. Phys. 74, 096501 (2011)." href="/articles/s41524-020-00482-5#ref-CR14" id="ref-link-section-d112338150e2549">14</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 50" title="Bauer, D. S. G. Development of a relativistic full-potential first-principles multiple scattering Green function method applied to complex magnetic textures of nano structures at surfaces. Ph.D. thesis, RWTH Aachen University (2013)." href="/articles/s41524-020-00482-5#ref-CR50" id="ref-link-section-d112338150e2552">50</a></sup>. This is achieved making use of the Dyson equation</p><div id="Equ3" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${G}^{{\rm{imp}}}={G}^{{\rm{host}}}+{G}^{{\rm{host}}}\ {{\Delta }}V{G}^{{\rm{imp}}}$$</span></div><div class="c-article-equation__number"> (3) </div></div><p>where <i>G</i><sup>host</sup> is the Green function of the crystalline host system, Δ<i>V</i> = <i>V</i><sup>imp</sup> − <i>V</i><sup>host</sup> is the difference in the potential introduced due to the presence of the impurity and <i>G</i><sup>imp</sup> is the Green function that describes the impurity embedded into the periodic host crystal. It is important to mention that the change in the potential Δ<i>V</i> occurs only in a small region around the impurity which is why the Dyson equation can be solved in a small real space region around the impurity site. This <i>impurity cluster</i> contains a few neighboring shells of host atoms that are necessary to properly treat the charge screening of the impurity by the neighboring host atoms. It is worthwhile noting that <i>G</i><sup>imp</sup> contains the complete information on physical properties like the DOS which is computed as <span class="mathjax-tex">$\rho ({\boldsymbol{r}};E)=-\frac{1}{\pi }{\rm{Im}}{\rm{Tr}}{G}^{{\rm{imp}}}({\boldsymbol{r}},{\boldsymbol{r}};E)$</span> (the trace is implied over spin-, atom- and orbital momentum degrees of freedom of the Green function). This impurity embedding scheme assumes a single impurity embedded into the infinite host crystal and therefore locally breaks the translational invariance. Such a calculation is typically done for the dilute limit of defects where the Fermi level is assumed to be fixed by the host crystal. The embedded defect is then allowed to transfer charge to and from the surrounding atoms of the host crystal that are included in the impurity cluster. The collective effect of changing Fermi level can then be included by using the host Green function computed for shifted Fermi level which can affect the impurity’s charge state and may strongly affect the crystal’s overall charge doping<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 45" title="Van de Walle, C. G. & Neugebauer, J. First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys. 95, 3851 (2004)." href="/articles/s41524-020-00482-5#ref-CR45" id="ref-link-section-d112338150e2772">45</a></sup>.</p><p>In summary, an impurity embedding calculation in the KKR formalism therefore consists of (i) calculating <i>G</i><sup>host</sup> (from a converged host calculation), (ii) creating Δ<i>V</i>, (iii) performing a self-consistent field cycle (scf) to converge <i>G</i><sup>imp</sup>.</p></div></div></section> </div> <div> <section data-title="Data availability"><div class="c-article-section" id="data-availability-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="data-availability">Data availability</h2><div class="c-article-section__content" id="data-availability-content"> <p>The data generated and analysed during the current study are available in the materialscloud archive<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="Rüßmann, P., Bertoldo, F. & Blügel, S. The JuDiT database of impurities embedded into a Topological Insulator. Materials Cloud Archive 2020.0030/v1 
 https://doi.org/10.24435/materialscloud:nq-ht
 
 (2020)." href="/articles/s41524-020-00482-5#ref-CR29" id="ref-link-section-d112338150e2851">29</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 51" title="Talirz, L. et al. Materials Cloud, a platform for open computational science. Sci. Data 7, 299 (2020)." href="/articles/s41524-020-00482-5#ref-CR51" id="ref-link-section-d112338150e2854">51</a></sup>. The JuDiT web interface<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Rüßmann, P., Bertoldo, F. & Blügel, S. JuDiT Database Discover section. 
 https://pgi-jcns.fz-juelich.de/judit
 
 (2020)." href="/articles/s41524-020-00482-5#ref-CR30" id="ref-link-section-d112338150e2858">30</a></sup> is published at <a href="https://www.materialscloud.org/discover">https://www.materialscloud.org/discover</a>. The figures of this work can be reproduced with the tools developed for the JuDiT web interface<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Rüßmann, P., Bertoldo, F. & Blügel, S. JuDiT Database Discover section. 
 https://pgi-jcns.fz-juelich.de/judit
 
 (2020)." href="/articles/s41524-020-00482-5#ref-CR30" id="ref-link-section-d112338150e2869">30</a></sup>.</p> </div></div></section><section data-title="Code availability"><div class="c-article-section" id="code-availability-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="code-availability">Code availability</h2><div class="c-article-section__content" id="code-availability-content"> <p>The sourcecode of the AiiDA-KKR plugin<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="The AiiDA-KKR developers. The AiiDA-KKR plugin for the JuKKR codes. 
 https://github.com/JuDFTteam/aiida-kkr
 
 ; 
 https://doi.org/10.5281/zenodo.3628251
 
 (2020)." href="/articles/s41524-020-00482-5#ref-CR9" id="ref-link-section-d112338150e2881">9</a></sup> is published as open source software under the MIT license at <a href="https://github.com/JuDFTteam/aiida-kkr">https://github.com/JuDFTteam/aiida-kkr</a>. The source code of the JuDiT web interface<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Rüßmann, P., Bertoldo, F. & Blügel, S. JuDiT Database Discover section. 
 https://pgi-jcns.fz-juelich.de/judit
 
 (2020)." href="/articles/s41524-020-00482-5#ref-CR30" id="ref-link-section-d112338150e2892">30</a></sup> with its visualization capabilities is open source under the MIT license as well and can be found at <a href="https://github.com/PhilippRue/JuDiT-discover-section">https://github.com/PhilippRue/JuDiT-discover-section</a>.</p> </div></div></section><div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">Villars, P., Cenzual, K., Gladyshevskii, R. & Iwata, S. 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PR and SB acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 - 390534769. This work was supported by computing time granted by the JARA Vergabegremium and provided on the JARA Partition part of the supercomputer CLAIX at RWTH Aachen University. P.R. would like to thank P. Mavropoulos, J. Bröder, and the AiiDA-team for fruitful discussions.</p></div></div></section><section data-title="Funding"><div class="c-article-section" id="Fun-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Fun">Funding</h2><div class="c-article-section__content" id="Fun-content"><p>Open Access funding enabled and organized by Projekt DEAL.</p></div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425, Jülich, Germany</p><p class="c-article-author-affiliation__authors-list">Philipp Rüßmann, Fabian Bertoldo & Stefan Blügel</p></li></ol><div class="u-js-hide u-hide-print" data-test="author-info"><span class="c-article__sub-heading">Authors</span><ol class="c-article-authors-search u-list-reset"><li id="auth-Philipp-R__mann-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Philipp Rüßmann</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Philipp%20R%C3%BC%C3%9Fmann" class="c-article-button" data-track="click" data-track-action="author link - 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P.R. and F.B. developed the AiiDA-KKR plugin. P.R. performed the calculations, developed the JuDiT webinterface for the data analysis, and wrote the initial manuscript. All authors contributed to the final manuscript.</p><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding author</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:p.ruessmann@fz-juelich.de">Philipp Rüßmann</a>.</p></div></div></section><section data-title="Ethics declarations"><div class="c-article-section" id="ethics-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="ethics">Ethics declarations</h2><div class="c-article-section__content" id="ethics-content"> <h3 class="c-article__sub-heading" id="FPar1">Competing interests</h3> <p>The authors declare no competing interests.</p> </div></div></section><section data-title="Additional information"><div class="c-article-section" id="additional-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="additional-information">Additional information</h2><div class="c-article-section__content" id="additional-information-content"><p><b>Publisher’s note</b> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></div></div></section><section data-title="Supplementary information"><div class="c-article-section" id="Sec9-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec9">Supplementary information</h2><div class="c-article-section__content" id="Sec9-content"><div data-test="supplementary-info"><div id="figshareContainer" class="c-article-figshare-container" data-test="figshare-container"></div><div class="c-article-supplementary__item" data-test="supp-item" id="MOESM1"><h3 class="c-article-supplementary__title u-h3"><a class="print-link" data-track="click" data-track-action="view supplementary info" data-test="supp-info-link" data-track-label="supplementary information" href="https://static-content.springer.com/esm/art%3A10.1038%2Fs41524-020-00482-5/MediaObjects/41524_2020_482_MOESM1_ESM.pdf" data-supp-info-image="">Supplementary Information</a></h3></div></div></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"> <p><b>Open Access</b> This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 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