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class="existingWikiWord" href="/nlab/show/crystallographic+group">crystallographic group</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bravais+lattice">Bravais lattice</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bloch+theory">Bloch theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/electronic+band+structure">electronic band structure</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/valence+bundle">valence bundle</a>, <a class="existingWikiWord" href="/nlab/show/conduction+bundle">conduction bundle</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/valence+band">valence band</a>, <a class="existingWikiWord" href="/nlab/show/conduction+band">conduction band</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Berry+connection">Berry connection</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Berry+phase">Berry phase</a>, <a class="existingWikiWord" href="/nlab/show/Zak+phase">Zak phase</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/phase+of+matter">phase of matter</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/insulator">insulator</a>, <a class="existingWikiWord" href="/nlab/show/topological+insulator">topological insulator</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/metal">metal</a>/<a class="existingWikiWord" href="/nlab/show/conductor">conductor</a>, <a class="existingWikiWord" href="/nlab/show/semi-conductor">semi-conductor</a>, <a class="existingWikiWord" href="/nlab/show/semi-metal">semi-metal</a>,</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/superconductor">superconductor</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/strange+metal">strange metal</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+phase+of+matter">topological phase of matter</a>, <a class="existingWikiWord" href="/nlab/show/topological+state+of+matter">topological state of matter</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/symmetry+protected+topological+phase">symmetry protected topological phase</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/K-theory+classification+of+topological+phases+of+matter">K-theory classification of topological phases of matter</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+order">topological order</a></p> <p><a class="existingWikiWord" href="/nlab/show/anyons">anyons</a></p> </li> <li> <p>Examples</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/graphene">graphene</a>, <a class="existingWikiWord" href="/nlab/show/Haldane+model">Haldane model</a>,</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+Hall+effect">quantum Hall effect</a>)</p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/AdS-CFT+in+condensed+matter+physics">AdS-CFT in condensed matter physics</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/tensor+network+state">tensor network state</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Levin-Wen+model">Levin-Wen model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Josephson+effect">Josephson effect</a></p> </li> </ul> </div></div> <h4 id="topological_physics">Topological physics</h4> <div class="hide"><div> <p><strong>Topological Physics</strong> – Phenomena in <a class="existingWikiWord" href="/nlab/show/physics">physics</a> controlled by the <a class="existingWikiWord" href="/nlab/show/topology">topology</a> (often: the <a class="existingWikiWord" href="/nlab/show/homotopy+theory">homotopy theory</a>) of the <a class="existingWikiWord" href="/nlab/show/physical+system">physical system</a>.</p> <p>General theory:</p> <ul> <li> <p>(<a class="existingWikiWord" href="/nlab/show/extended+topological+field+theory">extended</a>) <a class="existingWikiWord" href="/nlab/show/topological+field+theory">topological field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Chern-Simons+theory">Chern-Simons theory</a></p> </li> </ul> <p>In <a class="existingWikiWord" href="/nlab/show/solid+state+physics">solid state physics</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+state+of+matter">topological state of matter</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+material">quantum material</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gapped+Hamiltonian">gapped Hamiltonian</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+order">topological order</a>, <a class="existingWikiWord" href="/nlab/show/symmetry+protected+trivial+order">symmetry protected trivial order</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+insulator">topological insulator</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+Hall+effect">quantum Hall effect</a>, <a class="existingWikiWord" href="/nlab/show/quantum+spin+Hall+effect">quantum spin Hall effect</a></p> <p><a class="existingWikiWord" href="/nlab/show/anyons">anyons</a>, <a class="existingWikiWord" href="/nlab/show/braid+group+statistics">braid group statistics</a></p> </li> </ul> </li> </ul> <p>In <a class="existingWikiWord" href="/nlab/show/metamaterials">metamaterials</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+photonics">topological photonics</a> (<a class="existingWikiWord" href="/nlab/show/light+waves">light waves</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+phononics">topological phononics</a> (<span class="newWikiWord">sound waves<a href="/nlab/new/sound+waves">?</a></span>)</p> </li> </ul> <p>For <a class="existingWikiWord" href="/nlab/show/quantum+computation">quantum computation</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/topological+quantum+computation">topological quantum computation</a></li> </ul> <p>In <a class="existingWikiWord" href="/nlab/show/quantum+hadrodynamics">quantum hadrodynamics</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Skyrmion">Skyrmion</a></li> </ul> <p>In <a class="existingWikiWord" href="/nlab/show/quantum+chromodynamics">quantum chromodynamics</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/instanton">instanton</a></li> </ul> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#related_concepts'>Related concepts</a></li> <li><a href='#references'>References</a></li> <ul> <li><a href='#general'>General</a></li> <li><a href='#berry_connection'>Berry connection</a></li> <li><a href='#ReferencesMovementOfDiracPoints'>Movement of Dirac points</a></li> <li><a href='#holographic_description'>Holographic description</a></li> </ul> </ul> </div> <h2 id="idea">Idea</h2> <p>Graphene is one of the <a class="existingWikiWord" href="/nlab/show/solid">solid</a> <a class="existingWikiWord" href="/nlab/show/phase+of+matter">phases</a> of <a class="existingWikiWord" href="/nlab/show/carbon">carbon</a>, appearing as a single-layer honeycomb lattice. This may be planar or tubular, etc.</p> <p id="PrimeExampleOfTopologicalPhase"> Graphene is a prime example (and among the first to be discovered) of a <a class="existingWikiWord" href="/nlab/show/topological+phase+of+matter">topological phase of matter</a>. Specifically:</p> <ol> <li> <p>at coarse resolution (currently accessible to <a class="existingWikiWord" href="/nlab/show/experiment">experiment</a>) it appears as a (<a class="existingWikiWord" href="/nlab/show/time-reversal+symmetry">time-reversal</a> and space inversion-symmetric) <a class="existingWikiWord" href="/nlab/show/topological+semi-metal">topological semi-metal</a>, due to a gap between its <a class="existingWikiWord" href="/nlab/show/valence+band">valence band</a> and <a class="existingWikiWord" href="/nlab/show/conduction+band">conduction band</a> which closes only over two <a class="existingWikiWord" href="/nlab/show/Dirac+points">Dirac points</a> in its <a class="existingWikiWord" href="/nlab/show/Brillouin+torus">Brillouin torus</a>;</p> </li> <li> <p>at finer resolution – namely when the <a class="existingWikiWord" href="/nlab/show/spin-orbit+coupling">spin-orbit coupling</a> of the <a class="existingWikiWord" href="/nlab/show/electrons">electrons</a> is resolved (thought to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo>∼</mo><msup><mn>10</mn> <mrow><mo lspace="verythinmathspace" rspace="0em">−</mo><mn>3</mn></mrow></msup><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\sim10^{-3}\,</annotation></semantics></math><a class="existingWikiWord" href="/nlab/show/meV">meV</a> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="#MHSSKM06">MHSSKM06</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math> and hence too small for <a class="existingWikiWord" href="/nlab/show/experiment">experimental</a> observation, currently), which reveals a small energy gap opening at the two would-be Dirac points – graphene appears as a (<a class="existingWikiWord" href="/nlab/show/time-reversal+symmetry">time-reversal symmetric</a>) <a class="existingWikiWord" href="/nlab/show/topological+insulator">topological insulator</a> (<a href="#KaneMele05a">Kane & Mele 05a</a>), whose non-trivial <a class="existingWikiWord" href="/nlab/show/topological+phase+of+matter">topological phase</a> is witnessed by the non-trivial <a class="existingWikiWord" href="/nlab/show/Kane-Mele+invariant">Kane-Mele invariant</a> in <a class="existingWikiWord" href="/nlab/show/cyclic+group+of+order+two"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mi>ℤ</mi> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> <annotation encoding="application/x-tex">\mathbb{Z}/2</annotation> </semantics> </math></a> (<a href="#KaneMele05b">Kane & Mele 05b</a>).</p> </li> </ol> <h2 id="related_concepts">Related concepts</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/goldene">goldene</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+material">quantum material</a></p> </li> </ul> <h2 id="references">References</h2> <h3 id="general">General</h3> <p>The <a class="existingWikiWord" href="/nlab/show/electronic+band+structure">electronic band structure</a> of graphene (reviewed in <a href="#WZLLJHD12">WZLLJHD 12</a>) was predicted (long before the term was coined) already in</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Philip+Russel+Wallace">Philip Russel Wallace</a>, <em>The Band Theory of Graphite</em>, Phys. Rev. <strong>71</strong> (1947) 622 (<a href="https://doi.org/10.1103/PhysRev.71.622">doi:10.1103/PhysRev.71.622</a>)</li> </ul> <p>The synthesis/detection of graphene is due to</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Konstantin+Novoselov">Konstantin Novoselov</a>, <a class="existingWikiWord" href="/nlab/show/Andre+Geim">Andre Geim</a>, S. V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, <em>Electric field effect in atomically thin carbon films</em>, Science <strong>306</strong>, no. 5696, pp. 666-669 (2004) (<a href="http://dx.doi.org/10.1126/science.1102896">doi:10.1126/science.1102896</a>, <a href="https://arxiv.org/abs/cond-mat/0410550">arXiv:cond-mat/0410550</a>)</li> </ul> <p>(The procedure, won a Nobel Prize and the authors made it freely available without patenting.)</p> <p>Further discussion of the <a class="existingWikiWord" href="/nlab/show/electron+band+structure">electron band structure</a> of graphene:</p> <ul> <li>A. H. Castro Neto, F. Guinea, N. M. R. Peres, <a class="existingWikiWord" href="/nlab/show/Konstantin+S.+Novoselov">Konstantin S. Novoselov</a>, and <a class="existingWikiWord" href="/nlab/show/Andre+K.+Geim">Andre K. Geim</a>, <em>The electronic properties of graphene</em>, Rev. Mod. Phys. <strong>81</strong> (2009) 109 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://doi.org/10.1103/RevModPhys.81.109">doi:10.1103/RevModPhys.81.109</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></li> </ul> <p>Computation of the (tiny) <a class="existingWikiWord" href="/nlab/show/spin-orbit+coupling">spin-orbit coupling</a> in graphene:</p> <ul> <li id="MHSSKM06">Hongki Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, Leonard Kleinman, A. H. MacDonald, <em>Intrinsic and Rashba spin-orbit interactions in graphene sheets</em>, Phys. Rev. B <strong>74</strong> (2006) 165310 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://doi.org/10.1103/PhysRevB.74.165310">doi:10.1103/PhysRevB.74.165310</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></li> </ul> <p>Observation that the <a class="existingWikiWord" href="/nlab/show/spin-orbit+coupling">spin-orbit coupling</a> in graphene should open the gap at the <a class="existingWikiWord" href="/nlab/show/Dirac+points">Dirac points</a> revealing a <a class="existingWikiWord" href="/nlab/show/quantum+spin+Hall+effect">quantum spin Hall effect</a> in graphene:</p> <ul> <li id="KaneMele05a"> <p><a class="existingWikiWord" href="/nlab/show/Charles+Kane">Charles Kane</a>, <a class="existingWikiWord" href="/nlab/show/Eugene+Mele">Eugene Mele</a>, <em>Quantum Spin Hall Effect in Graphene</em>, Phys. Rev. Lett. 95, 226801 (2005) (<a href="https://arxiv.org/abs/cond-mat/0411737">arXiv:cond-mat/0411737</a>, <a href="https://doi.org/10.1103/PhysRevLett.95.226801">doi:10.1103/PhysRevLett.95.226801</a>)</p> </li> <li id="KaneMele05b"> <p><a class="existingWikiWord" href="/nlab/show/Charles+Kane">Charles Kane</a>, <a class="existingWikiWord" href="/nlab/show/Eugene+Mele">Eugene Mele</a>, <em><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>Z</mi> <mn>2</mn></msub></mrow><annotation encoding="application/x-tex">Z_2</annotation></semantics></math> Topological Order and the Quantum Spin Hall Effect</em>, Phys. Rev. Lett. <strong>95</strong> (2005) 146802 (<a href="https://doi.org/10.1103/PhysRevLett.95.146802">doi:10.1103/PhysRevLett.95.146802</a>)</p> </li> </ul> <p>Review:</p> <ul> <li id="WZLLJHD12"> <p>Nathan Weiss, Hailong Zhou, Lei Liao, Yuan Liu, Shan Jiang, Yu Huang, Xiangfeng Duan, <em>Graphene: an emerging electronic material</em>, Adv Mater. <strong>24</strong> (43) (2012) 5782-825 (<a href="https://doi.org/10.1002/adma.201201482">doi:10.1002/adma.201201482</a>)</p> </li> <li> <p>Wikipedia, <em><a href="https://en.wikipedia.org/wiki/Graphene">Graphene</a></em></p> </li> </ul> <p>Review in the context of <a class="existingWikiWord" href="/nlab/show/topological+phases+of+matter">topological phases of matter</a> and specifically topological <a class="existingWikiWord" href="/nlab/show/semi-metals">semi-metals</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/J%C3%A9r%C3%B4me+Cayssol">Jérôme Cayssol</a>, <a class="existingWikiWord" href="/nlab/show/Jean-No%C3%ABl+Fuchs">Jean-Noël Fuchs</a>, Section 6 of: <em>Topological and geometrical aspects of band theory</em>, J. Phys. Mater. <strong>4</strong> (2021) 034007 (<a href="https://arxiv.org/abs/2012.11941">arXiv:2012.11941</a>, <a href="https://doi.org/10.1088/2515-7639/abf0b5">doi:10.1088/2515-7639/abf0b5</a>)</li> </ul> <p>The 2+1 dim <a class="existingWikiWord" href="/nlab/show/Dirac+equation">Dirac equation</a> is used in modeling graphene:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Konstantin+Novoselov">Konstantin Novoselov</a>, <a class="existingWikiWord" href="/nlab/show/Andre+Geim">Andre Geim</a>, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, <em>Two-dimensional gas of massless Dirac fermions in graphene</em>, Nature <strong>438</strong>, 197-200 (2005) <a href="http://dx.doi.org/10.1038/nature04233">doi</a></p> </li> <li> <p>María A. H. Vozmediano, <em>Renormalization group aspects of graphene</em>, <a href="http://www.isis.stfc.ac.uk/groups/theory/downloads/the-strong-correlations-puzzle8120.pdf">pdf</a></p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/non-perturbative+effects">non-perturbative effects</a> in graphene:</p> <ul> <li>Juan Angel Casimiro Olivares, Ana Julia Mizher, Alfredo Raya, <em>Non-perturbative field theoretical aspects of graphene and related systems</em> [<a href="https://arxiv.org/abs/2109.10420">arXi:2109.10420</a>]</li> </ul> <p>Discussion via <a class="existingWikiWord" href="/nlab/show/AdS-CFT+in+condensed+matter+physics">AdS-CFT in condensed matter physics</a>:</p> <ul> <li>Jeong-Won Seo, Taewon Yuk, Young-Kwon Han, Sang-Jin Sin, <em>ABC-stacked multilayer graphene in holography</em> [<a href="https://arxiv.org/abs/2208.14642">arXiv:2208.14642</a>]</li> </ul> <p>On fractional charges in graphene:</p> <ul> <li>Chang-Yu Hou, Claudio Chamon, Christopher Mudry, <em>Electron fractionalization in two-dimensional graphenelike structures</em>, Phys. Rev. Lett. <strong>98</strong> (2007) 186809 [<a href="https://arxiv.org/abs/cond-mat/0609740">arXiv:cond-mat/0609740</a>, <a href="
https://doi.org/10.1103/PhysRevLett.98.186809">doi:10.1103/PhysRevLett.98.186809</a>]</li> </ul> <h3 id="berry_connection">Berry connection</h3> <p>On “fictitious” contributions to the <a class="existingWikiWord" href="/nlab/show/Berry+connection">Berry connection</a> on the <a class="existingWikiWord" href="/nlab/show/Brillouin+torus">Brillouin torus</a> of graphene:</p> <ul> <li>Mircea Trif, Pramey Upadhyaya, Yaroslav Tserkovnyak, <em>Theory of electromechanical coupling in dynamical graphene</em>, Phys. Rev. B <strong>88</strong> 245423 (2013) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://doi.org/10.1103/PhysRevB.88.245423">doi:10.1103/PhysRevB.88.245423</a>, <a href="https://arxiv.org/abs/1210.7384">arXiv:1210.7384</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></li> </ul> <h3 id="ReferencesMovementOfDiracPoints">Movement of Dirac points</h3> <p>Moving the nodal points in graphene(-variants) by changing external parameters such as lattice anisotropy or <a class="existingWikiWord" href="/nlab/show/strain">strain</a> (see also further discussion of external manipulation by strain <a href="topological+insulator#ReferencesOnExternalManipulationViaStrain">here</a>, and see the <a href="braid+group+statistics#ReferencesAnyonicBraidingInMomentumSpace">references on momentum-space braiding</a> of band nodes):</p> <ul> <li> <p>Cui-Lian Lia, <em>New position of Dirac points in the strained graphene reciprocal lattice</em>, AIP Advances <strong>4</strong> (2014) 087119 [<a href="https://doi.org/10.1063/1.4893239">doi:10.1063/1.4893239</a>]</p> </li> <li> <p>Marc Dvoraka, Zhigang Wu, <em>Dirac point movement and topological phase transition in patterned graphene</em>, Nanoscale <strong>7</strong> (2015) 3645-3650 [<a href="https://doi.org/10.1039/C4NR06454B">doi:10.1039/C4NR06454B</a>]</p> </li> <li> <p>Zhenzhu Li, Zhongfan Liu, Zhirong Liu: <em>Movement of Dirac points and band gaps in graphyne under rotating strain</em>, Nano Research <strong>10</strong> (2017) 2005–2020 [<a href="https://doi.org/10.1007/s12274-016-1388-z">doi:10.1007/s12274-016-1388-z</a>]</p> </li> <li> <p>Jian Kang, Oskar Vafek, <em>Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene</em>, Phys. Rev. B <strong>102</strong> (2020) 035161 [<a href="https://arxiv.org/abs/2002.10360">arXiv:2002.10360</a>, <a href="https://doi.org/10.1103/PhysRevB.102.035161">doi:10.1103/PhysRevB.102.035161</a>]</p> </li> </ul> <p>Movement of Dirac points in a cousin of the <a class="existingWikiWord" href="/nlab/show/Haldane+model">Haldane model</a>:</p> <ul> <li>Miguel Gonçalves, Pedro Ribeiro, Eduardo V. Castro, <em>Dirac points merging and wandering in a model Chern insulator</em>, Europhysics Letters <strong>124</strong> 6 (2018) [<a href="https://iopscience.iop.org/article/10.1209/0295-5075/124/67003">doi:10.1209/0295-5075/124/67003</a>]</li> </ul> <p>and in <a class="existingWikiWord" href="/nlab/show/photonic+crystal">photonic crystal</a>-analogs:</p> <ul> <li>Yong-Heng Lu et al., <em>Observing movement of Dirac cones from single-photon dynamics</em>, Phys. Rev. B <strong>103</strong> 064304 (2021) [<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.064304">doi:10.1103/PhysRevB.103.064304</a>]</li> </ul> <h3 id="holographic_description">Holographic description</h3> <p>On <a class="existingWikiWord" href="/nlab/show/AdS-CMT+duality">AdS-CMT duality</a> for graphene-like systems via full <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> (retaining the <a class="existingWikiWord" href="/nlab/show/gravitino">gravitino</a>):</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Laura+Andrianopoli">Laura Andrianopoli</a>, <a class="existingWikiWord" href="/nlab/show/Bianca+L.+Cerchiai">Bianca L. Cerchiai</a>, <a class="existingWikiWord" href="/nlab/show/Riccardo+D%27Auria">Riccardo D'Auria</a>, <a class="existingWikiWord" href="/nlab/show/Mario+Trigiante">Mario Trigiante</a>, <em>Unconventional Supersymmetry at the Boundary of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>AdS</mi> <mn>4</mn></msub></mrow><annotation encoding="application/x-tex">AdS_4</annotation></semantics></math> Supergravity</em>, J. High Energ. Phys. <strong>2018</strong> 7 (2018) [<a href="https://arxiv.org/abs/1801.08081">arXiv:1801.08081</a>, <a href="https://doi.org/10.1007/JHEP04(2018)007">doi:10.1007/JHEP04(2018)007</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Laura+Andrianopoli">Laura Andrianopoli</a>, <a class="existingWikiWord" href="/nlab/show/Bianca+L.+Cerchiai">Bianca L. Cerchiai</a>, <a class="existingWikiWord" href="/nlab/show/Riccardo+D%27Auria">Riccardo D'Auria</a>, A. Gallerati, R. Noris, <a class="existingWikiWord" href="/nlab/show/Mario+Trigiante">Mario Trigiante</a>, <a class="existingWikiWord" href="/nlab/show/Jorge+Zanelli">Jorge Zanelli</a>, <em><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>𝒩</mi></mrow><annotation encoding="application/x-tex">\mathcal{N}</annotation></semantics></math>-Extended <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>D</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">D=4</annotation></semantics></math> Supergravity, Unconventional SUSY and Graphene</em>, JHEP 01 (2020) 084 [<a href="https://arxiv.org/abs/1910.03508">arXiv:1910.03508</a>, <a href="https://doi.org/10.1007/JHEP01(2020)084">doi:10.1007/JHEP01(2020)084</a>]</p> </li> <li> <p>Antonio Gallerati, <em>Supersymmetric theories and graphene</em>, in <em>40th International Conference on High Energy physics</em> (ICHEP2020), PoS <strong>390</strong> (2021) [<a href="https://arxiv.org/abs/2104.07420">arXiv:2104.07420</a>, <a href="https://doi.org/10.22323/1.390.0662">doi:10.22323/1.390.0662</a>]</p> </li> </ul> <p>Exposition:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Bianca+L.+Cerchiai">Bianca L. Cerchiai</a>, <em>Supergravity in a pencil</em>, <a href="M-Theory+and+Mathematics#Cerchiai2020">talk at</a> <em><a class="existingWikiWord" href="/nlab/show/M-Theory+and+Mathematics">M-Theory and Mathematics</a> <a href="M-Theory+and+Mathematics#2020">2020</a></em>, NYU Abu Dhabi [<a class="existingWikiWord" href="/nlab/files/CerchiaiSlidesAtMTheoryAndMathematics2020.pdf" title="pdf slides">pdf slides</a>, video: <a href="https://youtu.be/xE7TmwyqqaU">YT</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bianca+L.+Cerchiai">Bianca L. Cerchiai</a>, <em>Holography, Supergravity and Graphene</em>, talk at <em>106th online SIF Congress</em> (2020) [<a href="https://agenda.infn.it/event/23656/contributions/120378/attachments/75347/96340/cerchiai_sif2020.pdf">pdf</a>, <a class="existingWikiWord" href="/nlab/files/Cerciai-SIF2020.pdf" title="pdf">pdf</a>&r</p> </li> </ul> <div class="property">category: <a class="category_link" href="/nlab/all_pages/physics">physics</a></div></body></html> </div> <div class="revisedby"> <p> Last revised on June 9, 2024 at 20:11:54. See the <a href="/nlab/history/graphene" style="color: #005c19">history</a> of this page for a list of all contributions to it. </p> </div> <div class="navigation navfoot"> <a href="/nlab/edit/graphene" accesskey="E" class="navlink" id="edit" rel="nofollow">Edit</a><a href="https://nforum.ncatlab.org/discussion/12324/#Item_6">Discuss</a><span class="backintime"><a href="/nlab/revision/graphene/19" accesskey="B" class="navlinkbackintime" id="to_previous_revision" rel="nofollow">Previous revision</a></span><a href="/nlab/show/diff/graphene" accesskey="C" class="navlink" id="see_changes" rel="nofollow">Changes from previous revision</a><a href="/nlab/history/graphene" accesskey="S" class="navlink" id="history" rel="nofollow">History (19 revisions)</a> <a href="/nlab/show/graphene/cite" style="color: black">Cite</a> <a href="/nlab/print/graphene" accesskey="p" id="view_print" rel="nofollow">Print</a> <a href="/nlab/source/graphene" id="view_source" rel="nofollow">Source</a> </div> </div>  </div>  </body> </html>