Introduction to Dirac materials and topological insulators

Jérôme Cayssol

doi:10.1016/j.crhy.2013.09.012

Topological insulators/Isolants topologiques

Introduction to Dirac materials and topological insulators
[Introduction aux matériaux de Dirac et aux isolants topologiques]

Jérôme Cayssol ^1,²

¹ Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany
² LOMA (UMR 5798), CNRS and University Bordeaux-1, 33045 Talence, France

Comptes Rendus. Physique, Topological insulators / Isolants topologiques, Volume 14 (2013) no. 9-10, pp. 760-778.

Résumé
Abstract

Nous présentons dans cet article une courte introduction didactique à la physique des matériaux de Dirac, restreinte au graphène et à des isolants topologiques en deux dimensions. Nous commençons par un bref rappel des équations de Dirac et de Weyl dans le contexte de la physique des particules. Abordant les systèmes relatifs à la matière condensée, le graphène semi-métallique et divers isolants de Dirac sont présentés, parmi lesquels les isolants topologiques de Haldane et de Kane–Mele. Nous discutons aussi brièvement les réalisations expérimentales avec des matériaux à fort couplage spin–orbite.

We present a short pedagogical introduction to the physics of Dirac materials, restricted to graphene and two-dimensional topological insulators. We start with a brief reminder of the Dirac and Weyl equations in the particle physics context. Turning to condensed matter systems, semimetallic graphene and various Dirac insulators are introduced, including the Haldane and the Kane–Mele topological insulators. We also discuss briefly experimental realizations in materials with strong spin–orbit coupling.

Publié le : 2013-10-14

DOI : 10.1016/j.crhy.2013.09.012

Keywords: Dirac fermions, Graphene, Topological insulators, Edge modes
Mots-clés : Fermions de Dirac, Graphène, Isolants topologiques, États de bord

Affiliations des auteurs :

Jérôme Cayssol ^{1, 2}

¹ Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany
² LOMA (UMR 5798), CNRS and University Bordeaux-1, 33045 Talence, France

@article{CRPHYS_2013__14_9-10_760_0,
     author = {J\'er\^ome Cayssol},
     title = {Introduction to {Dirac} materials and topological insulators},
     journal = {Comptes Rendus. Physique},
     pages = {760--778},
     publisher = {Elsevier},
     volume = {14},
     number = {9-10},
     year = {2013},
     doi = {10.1016/j.crhy.2013.09.012},
     language = {en},
}

TY  - JOUR
AU  - Jérôme Cayssol
TI  - Introduction to Dirac materials and topological insulators
JO  - Comptes Rendus. Physique
PY  - 2013
SP  - 760
EP  - 778
VL  - 14
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crhy.2013.09.012
LA  - en
ID  - CRPHYS_2013__14_9-10_760_0
ER  -

%0 Journal Article
%A Jérôme Cayssol
%T Introduction to Dirac materials and topological insulators
%J Comptes Rendus. Physique
%D 2013
%P 760-778
%V 14
%N 9-10
%I Elsevier
%R 10.1016/j.crhy.2013.09.012
%G en
%F CRPHYS_2013__14_9-10_760_0

Jérôme Cayssol. Introduction to Dirac materials and topological insulators. Comptes Rendus. Physique, Topological insulators / Isolants topologiques, Volume 14 (2013) no. 9-10, pp. 760-778. doi : 10.1016/j.crhy.2013.09.012. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.09.012/

Bibliographie
Cité par

[1] A. Zee Quantum Field Theory in a Nutshell, Princeton University Press, 2010

[2] S. Weinberg The Quantum Theory of Fields, Volume 1: Foundations, Cambridge University Press, 2005

[3] P.A.M. Dirac The quantum theory of the electron, P. Roy. Soc. Lond. Ser., Volume 117 (1928) no. 778, pp. 610-624

[4] P.A.M. Dirac A theory of electrons and protons, P. Roy. Soc. Lon. Ser.-A, Volume 126 (1930) no. 801, pp. 360-365

[5] O. Klein Z. Phys., 37 (1926), p. 895

[6] H. Weyl Electron and gravitation, Z. Phys., Volume 56 (1929), pp. 330-352

[7] E. Majorana Theory of the symmetry of electrons and positrons, Nuovo Cim., Volume 14 (1937), pp. 171-184

[8] P.B. Pal Dirac Majorana and Weyl fermions, 2010 | arXiv

[9] M.Z. Hasan; C.L. Kane Colloquium: Topological insulators, Rev. Mod. Phys., Volume 82 ( Nov. 2010 ), pp. 3045-3067

[10] Xiao-Liang Qi; Shou-Cheng Zhang Topological insulators and superconductors, Rev. Mod. Phys., Volume 83 ( Oct. 2011 ), pp. 1057-1110

[11] Markus König; Hartmut Buhmann; Laurens W. Molenkamp; Taylor Hughes; Chao-Xing Liu; Xiao-Liang Qi; Shou-Cheng Zhang The quantum spin Hall effect: theory and experiment, J. Phys. Soc. Jpn., Volume 77 ( March 2008 ) no. 3, p. 031007

[12] X.-L. Qi; S.-C. Zhang The quantum spin Hall effect and topological insulators, Phys. Today, Volume 63 (2010), p. 33

[13] B. Bernevig Topological Insulators and Topological Superconductors, Cambridge University Press, 2013

[14] C.L. Kane; E.J. Mele Quantum spin Hall effect in graphene, Phys. Rev. Lett., Volume 95 (2005), p. 226801

[15] C.L. Kane; E.J. Mele Topological order and the quantum spin Hall effect, Phys. Rev. Lett., Volume 95 (2005), p. 146802

[16] Frank T. Avignone; Steven R. Elliott; Jonathan Engel Double beta decay, Majorana neutrinos, and neutrino mass, Rev. Mod. Phys., Volume 80 ( Apr. 2008 ), pp. 481-516

[17] K.S. Novoselov; A.K. Geim; S.V. Morosov; D. Jiang; Y. Zhang; S.V. Dubonos; I.V. Grigorieva; A.A. Firsov Electric field effect in atomically thin carbon films, Science, Volume 306 (2004), p. 666

[18] K.S. Novoselov; A.K. Geim; S.V. Morosov; D. Jiang; M.I. Katsnelson; S.V. Grigorieva; I.V. Dubonos; A.A. Firsov Two-dimensional gas of massless Dirac fermions in graphene, Nature, Volume 438 (2005), p. 197

[19] Y. Zhang; Y.-W. Tan; H.L. Stormer; P. Kim Experimental observation of the quantum Hall effect and Berryʼs phase in graphene, Nature, Volume 438 (2005), p. 201

[20] P.R. Wallace The band theory of graphite, Phys. Rev., Volume 71 ( May 1947 ), pp. 622-634

[21] D.P. DiVincenzo; E.J. Mele Self-consistent effective-mass theory for intralayer screening in graphite intercalation compounds, Phys. Rev. B, Volume 29 ( Feb. 1984 ), pp. 1685-1694

[22] Gordon W. Semenoff Condensed-matter simulation of a three-dimensional anomaly, Phys. Rev. Lett., Volume 53 (1984), p. 2449

[23] F.D.M. Haldane Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett., Volume 61 (1988), p. 2015

[24] O. Klein Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac, Z. Phys., Volume 53 (1929), pp. 3-4

[25] Vadim V. Cheianov; Vladimir I. Falʼko Selective transmission of Dirac electrons and ballistic magnetoresistance of $n – p$ junctions in graphene, Phys. Rev. B, Volume 74 ( Jul. 2006 ), p. 041403

[26] M.I. Katsnelson; K.S. Novoselov; A.K. Geim Chiral tunnelling and the Klein paradox in graphene, Nat. Phys., Volume 2 (2006), p. 620 | DOI

[27] J. Cayssol; B. Huard; D. Goldhaber-Gordon Contact resistance and shot noise in graphene transistors, Phys. Rev. B, Volume 79 ( Feb. 2009 ), p. 075428

[28] Ai Yamakage; Ken-Ichiro Imura; Jérôme Cayssol; Yoshio Kuramoto Interfacial charge and spin transport in $Z_{2}$ topological insulators, Phys. Rev. B, Volume 83 (2011), p. 125401

[29] B. Huard; J.A. Sulpizio; N. Stander; K. Todd; B. Yang; D. Goldhaber-Gordon Transport measurements across a tunable potential barrier in graphene, Phys. Rev. Lett., Volume 98 ( Jun. 2007 ), p. 236803

[30] J.R. Williams; L. DiCarlo; C.M. Marcus Quantum Hall effect in a gate-controlled p–n junction of graphene, Science, Volume 317 (2007), p. 638

[31] Barbaros Özyilmaz; Pablo Jarillo-Herrero; Dmitri Efetov; Dmitry A. Abanin; Leonid S. Levitov; Philip Kim Electronic transport and quantum Hall effect in bipolar graphene $p – n – p$ junctions, Phys. Rev. Lett., Volume 99 ( Oct. 2007 ), p. 166804

[32] N. Stander; B. Huard; D. Goldhaber-Gordon Evidence for Klein tunneling in graphene $p – n$ junctions, Phys. Rev. Lett., Volume 102 ( Jan. 2009 ), p. 026807

[33] A.F. Young; P. Kim Quantum interference and carrier collimation in graphene heterojunctions, Nat. Phys., Volume 5 (2009), pp. 222-226

[34] T. Ando; T. Nakanishi; R. Saito Berryʼs phase and absence of back scattering in carbon nanotubes, J. Phys. Soc. Jpn., Volume 67 (1998), p. 2857

[35] P.E. Alain; J.N. Fuchs Klein tunneling in graphene: optics with massless electrons, Eur. Phys. J. B, Volume 83 (2011), pp. 301-317

[36] A.H. Castro Neto; F. Guinea; N.M.R. Peres; K.S. Novoselov; A.K. Geim The electronic properties of graphene, Rev. Mod. Phys., Volume 81 (2009), p. 109

[37] M.O. Goerbig Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys., Volume 83 (2011), p. 1193

[38] Valeri; N. Kotov; Bruno Uchoa; Vitor M. Pereira; F. Guinea; A.H. Castro Neto Electron–electron interactions in graphene: Current status and perspectives, Rev. Mod. Phys., Volume 84 ( Jul. 2012 ), pp. 1067-1125

[39] M.O. Goerbig; J.-N. Fuchs; G. Montambaux; F. Piéchon Phys. Rev. B, 78 ( Jul. 2008 ), p. 045415

[40] F. Guinea; M.I. Katsnelson; A.K. Geim Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering, Nat. Phys., Volume 6 (2010), p. 30

[41] Pouyan Ghaemi; Jérôme Cayssol; D.N. Sheng; Ashvin Vishwanath Fractional topological phases and broken time-reversal symmetry in strained graphene, Phys. Rev. Lett., Volume 108 ( Jun. 2012 ), p. 266801

[42] Shinsei Ryu; Christopher Mudry; Chang-Yu Hou; Claudio Chamon Masses in graphenelike two-dimensional electronic systems: Topological defects in order parameters and their fractional exchange statistics, Phys. Rev. B, Volume 80 (2009), p. 205319

[43] J. Zak Berryʼs phase for energy bands in solids, Phys. Rev. Lett., Volume 62 ( Jun. 1989 ), pp. 2747-2750

[44] L. Tarruell; D. Greif; T. Uehlinger; G. Jotzu; T. Esslinger Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature, Volume 483 (2012), p. 302

[45] E. Tang; J.-W. Mei; X.-G. Wen High-temperature fractional quantum Hall states, Phys. Rev. Lett., Volume 106 (2011), p. 236802

[46] K. Sun; Z. Gu; H. Katsura; S. Das Sarma Nearly flatbands with nontrivial topology, Phys. Rev. Lett., Volume 106 (2011), p. 236803

[47] T. Neupert; L. Santos; C. Chamon; C. Mudry Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett., Volume 106 (2011), p. 236804

[48] N. Regnault; B. Andrei Bernevig Fractional Chern insulator, Phys. Rev. X, Volume 1 (2011), p. 021014

[49] Y.-F. Wang; Z.-C. Gu; C.-D. Gong; D.N. Sheng Fractional quantum Hall effect of hard-core bosons in topological flat bands, Phys. Rev. Lett., Volume 107 (2011), p. 146803

[50] T. Neupert; L. Santos; S. Ryu; C. Chamon; C.ʼ Mudry Fractional topological liquids with time-reversal symmetry and their lattice realization, Phys. Rev. B, Volume 84 (2011), p. 165107

[51] C.-Z. Chang; J. Zhang; X. Feng; J. Shen; Z. Zhang; M. Guo; K. Li; Y. Ou; P. Wei; L.-L. Wang; Y. Feng; S. Ji; X. Chen; J. Jia; X. Dai; Z. Fang; S.-C. Zhang; K. He; Y. Wang; L. Lu; X.-C. Ma; Q.-K. Xue Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science, Volume 340 (2013) no. 6129, pp. 167-170

[52] Shuichi Murakami; Naoto Nagaosa; Shou-Cheng Zhang Dissipationless quantum spin current at room temperature, Science, Volume 301 (2003) no. 5638, pp. 1348-1351

[53] Jairo Sinova; Dimitrie Culcer; Q. Niu; N.A. Sinitsyn; T. Jungwirth; A.H. MacDonald Universal intrinsic spin Hall effect, Phys. Rev. Lett., Volume 92 ( Mar. 2004 ), p. 126603

[54] Y.K. Kato; R.C. Myers; A.C. Gossard; D.D. Awschalom Observation of the spin Hall effect in semiconductors, Science, Volume 306 (2004) no. 5703, pp. 1910-1913

[55] J. Wunderlich; B. Kaestner; J. Sinova; T. Jungwirth Experimental observation of the spin-Hall effect in a two-dimensional spin–orbit coupled semiconductor system, Phys. Rev. Lett., Volume 94 ( Feb. 2005 ), p. 047204

[56] Daniel Huertas-Hernando; F. Guinea; Arne Brataas Spin–orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps, Phys. Rev. B, Volume 74 ( Oct. 2006 ), p. 155426

[57] Hongki Min; J.E. Hill; N.A. Sinitsyn; B.R. Sahu; Leonard Kleinman; A.H. MacDonald Intrinsic and Rashba spin–orbit interactions in graphene sheets, Phys. Rev. B, Volume 74 ( Oct. 2006 ), p. 165310

[58] B.A. Bernevig; Taylor L. Hughes; Shou-Cheng Zhang Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science, Volume 314 (2006) no. 5806, p. 1757

[59] M. König; S. Wiedmann; C. Brüne; A. Roth; H. Buhmann; L.W. Molenkamp; X.L. Qi; S.C. Zhang Quantum spin Hall insulator state in HgTe quantum wells, Science, Volume 318 ( November 2007 ) no. 5851, pp. 766-770

[60] A. Roth; C. Brune; H. Buhmann; L.W. Molenkamp; J. Maciejko; X.L. Qi; S.C. Zhang Nonlocal transport in the quantum spin Hall state, Science, Volume 325 ( July 2009 ) no. 5938, pp. 294-297

[61] Chaoxing Liu; Taylor L. Hughes; Xiao-Liang Qi; Kang Wang; Shou-Cheng Zhang Quantum spin Hall effect in inverted type-ii semiconductors, Phys. Rev. Lett., Volume 100 ( Jun. 2008 ), p. 236601

[62] Ivan Knez; Rui-Rui Du; Gerard Sullivan Evidence for helical edge modes in inverted $InAs / GaSb$ quantum wells, Phys. Rev. Lett., Volume 107 ( Sep. 2011 ), p. 136603

[63] Chao-Xing Liu; Xiao-Liang Qi; Xi Dai; Zhong Fang; Shou-Cheng Zhang Quantum anomalous Hall effect in ${hg}_{1 - y} {mn}_{y} Te$ quantum wells, Phys. Rev. Lett., Volume 101 ( Oct. 2008 ), p. 146802

[64] Jing Wang; Biao Lian; Haijun Zhang; Shou-Cheng Zhang Anomalous edge transport in the quantum anomalous Hall state, Phys. Rev. Lett., Volume 111 ( Aug. 2013 ), p. 086803

[65] D.J. Thouless; M. Kohmoto; M.P. Nightingale; M. den Nijs Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett., Volume 49 ( Aug. 1982 ), pp. 405-408

[66] Xiao-Liang Qi; Yong-Shi Wu; Shou-Cheng Zhang Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Phys. Rev. B, Volume 74 ( Aug. 2006 ), p. 085308

[67] Doru Sticlet; Frederic Piéchon; Jean-Noël Fuchs; Pavel Kalugin; Pascal Simon Geometrical engineering of a two-band Chern insulator in two dimensions with arbitrary topological index, Phys. Rev. B, Volume 85 ( Apr. 2012 ), p. 165456

[68] R. Jackiw; C. Rebbi Solitons with fermion number 1/2, Phys. Rev. D, Volume 13 ( Jun. 1976 ), pp. 3398-3409

[69] W.P. Su; J.R. Schrieffer; A.J. Heeger Solitons in polyacetylene, Phys. Rev. Lett., Volume 42 ( Jun. 1979 ), pp. 1698-1701

[70] W.P. Su; J.R. Schrieffer; A.J. Heeger Soliton excitations in polyacetylene, Phys. Rev. B, Volume 22 ( Aug. 1980 ), pp. 2099-2111

[71] Takashi Oka; Hideo Aoki Photovoltaic Hall effect in graphene, Phys. Rev. B, Volume 79 (2009), p. 081406

[72] Takuya Kitagawa; Takashi Oka; Arne Brataas; Liang Fu; Eugene Demler Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels, Phys. Rev. B, Volume 84 ( Dec. 2011 ), p. 235108

[73] Zhenghao Gu; H.A. Fertig; Daniel P. Arovas; Assa Auerbach Floquet spectrum and transport through an irradiated graphene ribbon, Phys. Rev. Lett., Volume 107 ( Nov. 2011 ), p. 216601

[74] Manuel Torres; Alejandro Kunold Kubo formula for Floquet states and photoconductivity oscillations in a two-dimensional electron gas, Phys. Rev. B, Volume 71 ( Mar. 2005 ), p. 115313

[75] Netanel H. Lindner; Gil Refael; Victor Galitski Floquet topological insulator in semiconductor quantum wells, Nat. Phys., Volume 7 (2011), pp. 490-495

[76] J. Cayssol; B. Dora; F. Simon; R. Moessner Floquet topological insulators, Phys. Status Solidi, Volume 7 (2013) no. 1–2, pp. 101-108

[77] M. Polini; F. Guinea; M. Lewenstein; H.C. Manoharan; V. Pellegrini Artificial graphene as a tunable Dirac material, 2013 | arXiv

[78] K.K. Gomes; W. Mar; W. Ko; W. Guinea; H.C. Manoharan Designer Dirac fermions and topological phases in molecular graphene, Nature, Volume 483 (2012), p. 306

[79] A. Singha et al. Two-dimensional Mott–Hubbard electrons in an artificial honeycomb lattice, Science, Volume 332 (2011) no. 6034, pp. 1176-1179

[80] C.H. Park; S. Louie Making massless Dirac fermions from patterned two-dimensional electron gases, Nano Lett., Volume 9 (2009), pp. 1793-1797

[81] G.E. Volovik An analog of the quantum Hall effect in a superfluid ³He film, JETP, Volume 67 (1988), pp. 1804-1811

[82] G.E. Volovik, The Universe in a Helium Droplet, The International Series of Monographs on Physics, vol. 117, Oxford.

[83] A.B. Khanikaev; S.H. Mousavi; W.-K. Tse; M. Kargarian; A.H. MacDonald; G. Shvets Photonic topological insulators, Nature Materials, Volume 12 (2013), pp. 233-239

[84] M.C. Rechtsman; J.M. Zeuner; Y. Plotnik; Y. Lumer; D. Podolsky; F. Dreisow; S. Nolte; M. Segev; A. Szameit Photonic Floquet topological insulators, Nature, Volume 496 (2013), pp. 196-200

Alex E. Bernardini; R. da Rocha Algebraic solutions for SU(2)⊗SU(2) Hamiltonian eigensystems: Generic statistical ensembles and a mesoscopic system application, Annals of Physics, Volume 474 (2025), p. 169932 | DOI:10.1016/j.aop.2025.169932
François Fillion-Gourdeau; Emmanuel Lorin; Steve MacLean; Xu Yang Semi-classical limit of the Dirac equation in curved space and applications to strained and photonic graphene, Journal of Physics A: Mathematical and Theoretical, Volume 58 (2025) no. 11, p. 115302 | DOI:10.1088/1751-8121/adb402
Angira Roy; Ciaran P. Healey; Nathaniel E. Larm; Piyuni Ishtaweera; Maryuri Roca; Gary A. Baker The Huge Role of Tiny Impurities in Nanoscale Synthesis, ACS Nanoscience Au, Volume 4 (2024) no. 3, p. 176 | DOI:10.1021/acsnanoscienceau.3c00056
Karyn Le Hur; Sariah Al Saati Quantum Hall and Light Responses in a 2D Topological Semimetal, Comptes Rendus. Physique, Volume 25 (2024) no. G1, p. 415 | DOI:10.5802/crphys.202
Abhirup Mukherjee; Siddhartha Patra; Siddhartha Lal Holographic entanglement renormalisation for fermionic quantum matter, Journal of Physics A: Mathematical and Theoretical, Volume 57 (2024) no. 27, p. 275401 | DOI:10.1088/1751-8121/ad56e1
Sylvain Rossi; Alessandro Tarantola Topology of 2D Dirac operators with variable mass and an application to shallow-water waves, Journal of Physics A: Mathematical and Theoretical, Volume 57 (2024) no. 6, p. 065201 | DOI:10.1088/1751-8121/ad1d8e
Greeshma C Jose; Weiwei Xie; Barbara Lavina; Jiyong Zhao; Esen E Alp; Dongzhou Zhang; Wenli Bi Robust magnetism and crystal structure in Dirac semimetal EuMnBi2 under high pressure, Journal of Physics: Condensed Matter, Volume 36 (2024) no. 25, p. 255802 | DOI:10.1088/1361-648x/ad3473
Ashish Sharma; Anupma Thakur; V S Rangra Excitonic effects on the optical spectra of TiB2 nanosheets, Journal of Physics: Condensed Matter, Volume 36 (2024) no. 4, p. 045501 | DOI:10.1088/1361-648x/ad0353
O Ivanov; M Yaprintsev; E Yaprintseva; T Nickulicheva; A Vasil’ev Temperature evolution of transverse magnetoresistance due to forming the topological insulator state in single-crystalline n-type Bi2Te2.7Se0.3, Physica Scripta, Volume 99 (2024) no. 3, p. 035960 | DOI:10.1088/1402-4896/ad29cc
A. W. Romero Jorge; A. Pérez Martínez; E. Rodríguez Querts Nonlinear electrodynamics for the vacuum of Dirac materials: Photon magnetic properties and radiation pressures, Physical Review A, Volume 110 (2024) no. 1 | DOI:10.1103/physreva.110.012201
M. Inglot; J. Barnaś; V. K. Dugaev; A. Dyrdał Localized states at the Rashba spin-orbit domain wall in magnetized graphene: Interplay of Rashba and magnetic domain walls, Physical Review B, Volume 109 (2024) no. 13 | DOI:10.1103/physrevb.109.134435
Jeyson Támara-Isaza; Pablo Burset; William J. Herrera Microscopic Green's function approach for generalized Dirac Hamiltonians, Physical Review B, Volume 109 (2024) no. 19 | DOI:10.1103/physrevb.109.195405
Sina Kazemian; Giovanni Fanchini Influence of higher-order electron-phonon interaction on the electron-related lattice thermal properties of two-dimensional Dirac crystals, Physical Review B, Volume 109 (2024) no. 20 | DOI:10.1103/physrevb.109.205422
E. M. Wilson; J. T. Haraldsen Effects of frustration on the spin dynamics of the zigzag honeycomb lattice, Physical Review B, Volume 110 (2024) no. 6 | DOI:10.1103/physrevb.110.064429
Pradeep R. Varadwaj; Arpita Varadwaj; Helder Marques; Koichi Yamashita Fullerenes, carbon nanotubes and graphene as tetrel bond donors and acceptors of electrophiles, CrystEngComm, Volume 25 (2023) no. 23, p. 3417 | DOI:10.1039/d3ce00184a
Axel Schulze-Halberg Darboux algorithms for two-dimensional Dirac equations with upper triangular potential matrix, Journal of Computational and Applied Mathematics, Volume 427 (2023), p. 115143 | DOI:10.1016/j.cam.2023.115143
L Santamaría-Sanz One-dimensional scattering of fermions in double Dirac delta potentials, Journal of Physics A: Mathematical and Theoretical, Volume 56 (2023) no. 38, p. 385201 | DOI:10.1088/1751-8121/acef0d
Sina Kazemian; Giovanni Fanchini Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals, Journal of Physics: Condensed Matter, Volume 35 (2023) no. 32, p. 325601 | DOI:10.1088/1361-648x/acceee
L Ponvijayakanthan; Neeraj K Jaiswal; Haranath Ghosh Structural and electronic properties of novel BeN4/MgN4 nanoribbons, Nano Express, Volume 4 (2023) no. 4, p. 045006 | DOI:10.1088/2632-959x/ad04f8
L. Giovannini Dirac magnons in honeycomb nanostructures, Physical Review B, Volume 107 (2023) no. 10 | DOI:10.1103/physrevb.107.104418
Xi Chen; Klaus Zollner; Christian Moulsdale; Vladimir I. Fal'ko; Angelika Knothe Semimetallic and semiconducting graphene- hBN multilayers with parallel or reverse stacking, Physical Review B, Volume 107 (2023) no. 12 | DOI:10.1103/physrevb.107.125402
Alexander S. Sergeev Topological insulators and geometry of vector bundles, SciPost Physics Lecture Notes (2023) | DOI:10.21468/scipostphyslectnotes.67
Ilya Ivantsov; Alvaro Ferraz; Evgenii Kochetov Strong correlation, Bloch bundle topology, and spinless Haldane–Hubbard model, Annals of Physics, Volume 441 (2022), p. 168859 | DOI:10.1016/j.aop.2022.168859
N. Heidari; H. Hassanabadi; W. S. Chung Scattering state study of fermions due to q-deformed Dirac delta potential, Europhysics Letters, Volume 137 (2022) no. 6, p. 60002 | DOI:10.1209/0295-5075/ac6066
Ulf Saalmann; Jan Michael Rost Local excitation and valley polarization in graphene with multi-harmonic pulses, Faraday Discussions, Volume 237 (2022), p. 368 | DOI:10.1039/d2fd00017b
Abhinav Nag; Jagdish Kumar Spin-orbit coupling locked robust thermoelectric performance of SrTe: A comparison with CaTe, Materials Science and Engineering: B, Volume 276 (2022), p. 115581 | DOI:10.1016/j.mseb.2021.115581
M. Gomes; Pedro R. S. Gomes; K. Raimundo; Rodrigo Corso B. Santos; A. J. da Silva Topological superconductor from the quantum Hall phase: Effective field theory description, Physical Review B, Volume 106 (2022) no. 19 | DOI:10.1103/physrevb.106.195111
Xingchuan Zhu; Yiqun Huang; Huaiming Guo; Shiping Feng Quantum phase transitions from competing short- and long-range interactions on a π -flux lattice, Physical Review B, Volume 106 (2022) no. 7 | DOI:10.1103/physrevb.106.075109
Hamed Koochaki Kelardeh; Ulf Saalmann; Jan M. Rost Ultrashort laser-driven dynamics of massless Dirac electrons generating valley polarization in graphene, Physical Review Research, Volume 4 (2022) no. 2 | DOI:10.1103/physrevresearch.4.l022014
N K Karn; M M Sharma; V P S Awana Non-trivial band topology in the superconductor AuSn4: a first principle study, Superconductor Science and Technology, Volume 35 (2022) no. 11, p. 114002 | DOI:10.1088/1361-6668/ac9160
Bing-Sui Lu; Khatee Zathul Arifa; Martial Ducloy An excited atom interacting with a Chern insulator: toward a far-field resonant Casimir–Polder repulsion, The European Physical Journal D, Volume 76 (2022) no. 11 | DOI:10.1140/epjd/s10053-022-00544-x
Axel Schulze-Halberg Darboux transformations for Dirac equations in polar coordinates with vector potential and position-dependent mass, The European Physical Journal Plus, Volume 137 (2022) no. 7 | DOI:10.1140/epjp/s13360-022-03030-w
Axel Schulze-Halberg; Pinaki Roy Dirac systems with magnetic field and position-dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators, Annals of Physics, Volume 431 (2021), p. 168534 | DOI:10.1016/j.aop.2021.168534
Jiangming Cao; Zhi-Quan Huang; Gennevieve Macam; Yifan Gao; Naga Venkateswara Rao Nulakani; Xun Ge; Xiang Ye; Feng-Chuan Chuang; Li Huang Prediction of massless Dirac fermions in a carbon nitride covalent network, Applied Physics Letters, Volume 118 (2021) no. 13 | DOI:10.1063/5.0046069
Axel Schulze-Halberg Closed-form representations of iterated Darboux transformations for the massless Dirac equation, International Journal of Modern Physics A, Volume 36 (2021) no. 08n09, p. 2150064 | DOI:10.1142/s0217751x21500640
Axel Schulze-Halberg Characterization of Darboux transformations for quantum systems with quadratically energy-dependent potentials, Journal of Mathematical Physics, Volume 62 (2021) no. 8 | DOI:10.1063/5.0051739
J Cayssol; J N Fuchs Topological and geometrical aspects of band theory, Journal of Physics: Materials, Volume 4 (2021) no. 3, p. 034007 | DOI:10.1088/2515-7639/abf0b5
Musa A. M. Hussien; Aniekan Magnus Ukpong Electrodynamics of Topologically Ordered Quantum Phases in Dirac Materials, Nanomaterials, Volume 11 (2021) no. 11, p. 2914 | DOI:10.3390/nano11112914
Patrice Mélinon Vitreous Carbon, Geometry and Topology: A Hollistic Approach, Nanomaterials, Volume 11 (2021) no. 7, p. 1694 | DOI:10.3390/nano11071694
Mattis Reisner; Matthieu Bellec; Ulrich Kuhl; Fabrice Mortessagne Microwave resonator lattices for topological photonics [Invited], Optical Materials Express, Volume 11 (2021) no. 3, p. 629 | DOI:10.1364/ome.416835
Alexis Morvan; Mathieu Féchant; Gianluca Aiello; Julien Gabelli; Jérôme Estève Observation of topological valley Hall edge states in honeycomb lattices of superconducting microwave resonators, Optical Materials Express, Volume 11 (2021) no. 4, p. 1224 | DOI:10.1364/ome.414517
Axel Schulze-Halberg; Artur M Ishkhanyan Inverse-root and inverse-root-exponential potentials: Darboux transformations and elementary Darboux partners, Physica Scripta, Volume 96 (2021) no. 2, p. 025206 | DOI:10.1088/1402-4896/abcce5
Ganesh C. Paul; SK Firoz Islam; Paramita Dutta; Arijit Saha Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems, Physical Review B, Volume 103 (2021) no. 11 | DOI:10.1103/physrevb.103.115306
Jonathan Atteia; Mark Oliver Goerbig SU(4) spin waves in the ν=±1 quantum Hall ferromagnet in graphene, Physical Review B, Volume 103 (2021) no. 19 | DOI:10.1103/physrevb.103.195413
M. Inglot; V. K. Dugaev; A. Dyrdał; J. Barnaś Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall, Physical Review B, Volume 104 (2021) no. 21 | DOI:10.1103/physrevb.104.214408
B. Q. Lv; T. Qian; H. Ding Experimental perspective on three-dimensional topological semimetals, Reviews of Modern Physics, Volume 93 (2021) no. 2 | DOI:10.1103/revmodphys.93.025002
Axel Schulze-Halberg First-order Darboux transformations for Dirac equations with arbitrary diagonal potential matrix in two dimensions, The European Physical Journal Plus, Volume 136 (2021) no. 7 | DOI:10.1140/epjp/s13360-021-01804-2
Bing-Sui Lu The Casimir Effect in Topological Matter, Universe, Volume 7 (2021) no. 7, p. 237 | DOI:10.3390/universe7070237
Daniel Boyko; Avadh Saxena; Jason T. Haraldsen Spin Dynamics and Dirac Nodes in a Kagome Lattice, Annalen der Physik, Volume 532 (2020) no. 2 | DOI:10.1002/andp.201900350
Axel Schulze-Halberg; Artur M. Ishkhanyan Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation, Annals of Physics, Volume 421 (2020), p. 168273 | DOI:10.1016/j.aop.2020.168273
Axel Schulze-Halberg; Artur M. Ishkhanyan Exactly-Solvable Quantum Systems in Terms of Lambert-W Functions, Few-Body Systems, Volume 61 (2020) no. 2 | DOI:10.1007/s00601-020-1546-4
Axel Schulze-Halberg Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class, Journal of Mathematical Physics, Volume 61 (2020) no. 8 | DOI:10.1063/5.0013832
Jakub Šebesta; Karel Carva; Dominik Kriegner; Jan Honolka Twin Domain Structure in Magnetically Doped Bi2Se3 Topological Insulator, Nanomaterials, Volume 10 (2020) no. 10, p. 2059 | DOI:10.3390/nano10102059
Bing-Sui Lu; Khatee Zathul Arifa; Xing Ru Hong Spontaneous emission of a quantum emitter near a Chern insulator: Interplay of time-reversal symmetry breaking and Van Hove singularity, Physical Review B, Volume 101 (2020) no. 20 | DOI:10.1103/physrevb.101.205410
Yuanping Chen; Yuee Xie; Xiaohong Yan; Marvin L. Cohen; Shengbai Zhang Topological carbon materials: A new perspective, Physics Reports, Volume 868 (2020), p. 1 | DOI:10.1016/j.physrep.2020.05.003
Muhammad Nadeem; Alex R. Hamilton; Michael S. Fuhrer; Xiaolin Wang Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin‐Gapless Semiconductors—A Perspective Review, Small, Volume 16 (2020) no. 42 | DOI:10.1002/smll.201904322
Axel Schulze-Halberg Higher-order Darboux transformations for the Dirac equation with position-dependent mass at nonvanishing energy, The European Physical Journal Plus, Volume 135 (2020) no. 10 | DOI:10.1140/epjp/s13360-020-00882-y
Salvatore De Vincenzo On 3D and 1D Weyl particles in a 1D box, The European Physical Journal Plus, Volume 135 (2020) no. 10 | DOI:10.1140/epjp/s13360-020-00820-y
Axel Schulze-Halberg Arbitrary-order Darboux transformations for two-dimensional Dirac equations with position-dependent mass, The European Physical Journal Plus, Volume 135 (2020) no. 3 | DOI:10.1140/epjp/s13360-020-00345-4
Peng Cheng; Philipp W. Klein; Kirill Plekhanov; Klaus Sengstock; Monika Aidelsburger; Christof Weitenberg; Karyn Le Hur Topological proximity effects in a Haldane graphene bilayer system, Physical Review B, Volume 100 (2019) no. 8 | DOI:10.1103/physrevb.100.081107
Shahd Alfadhli; Fedor V. Kusmartsev; Sergey E. Savel’ev Manipulating the anisotropy of the Dirac-Cone in graphene by laser fields, The European Physical Journal B, Volume 92 (2019) no. 4 | DOI:10.1140/epjb/e2019-90668-x
William Borrelli Weakly localized states for nonlinear Dirac equations, Calculus of Variations and Partial Differential Equations, Volume 57 (2018) no. 6 | DOI:10.1007/s00526-018-1420-0
M. C. Onyeaju; A. N. Ikot; C. A. Onate; H. P. Obong; O. Ebomwonyi Scattering and Bound States of the Dirac Particle for q-Parameter Hyperbolic Pöschl-Teller Potential, Communications in Theoretical Physics, Volume 70 (2018) no. 5, p. 541 | DOI:10.1088/0253-6102/70/5/541
William Borrelli Multiple solutions for a self-consistent Dirac equation in two dimensions, Journal of Mathematical Physics, Volume 59 (2018) no. 4 | DOI:10.1063/1.5005998
D. Boyko; A. V. Balatsky; J. T. Haraldsen Evolution of magnetic Dirac bosons in a honeycomb lattice, Physical Review B, Volume 97 (2018) no. 1 | DOI:10.1103/physrevb.97.014433
Victor A. S. V. Bittencourt; Massimo Blasone; Alex E. Bernardini Bilayer graphene lattice-layer entanglement in the presence of non-Markovian phase noise, Physical Review B, Volume 97 (2018) no. 12 | DOI:10.1103/physrevb.97.125435
Sanju Gupta; Avadh Saxena Importance of Topology in Materials Science, The Role of Topology in Materials, Volume 189 (2018), p. 3 | DOI:10.1007/978-3-319-76596-9_1
Thomas La Martina; Jian‐Xin Zhu; Alexander V. Balatsky; Jason T. Haraldsen Dirac Nodes and Magnetic Order in M2X2 Transition‐Metal Chalcogenides, physica status solidi (RRL) – Rapid Research Letters, Volume 12 (2018) no. 11 | DOI:10.1002/pssr.201800181
Victor A. S. V. Bittencourt; Alex E. Bernardini Lattice-layer entanglement in Bernal-stacked bilayer graphene, Physical Review B, Volume 95 (2017) no. 19 | DOI:10.1103/physrevb.95.195145
Yizhou Liu; Yong Xu; Shou-Cheng Zhang; Wenhui Duan Model for topological phononics and phonon diode, Physical Review B, Volume 96 (2017) no. 6 | DOI:10.1103/physrevb.96.064106
M. C. Onyeaju; A. N. Ikot; C. A. Onate; O. Ebomwonyi; M. E. Udoh; J. O. A. Idiodi Approximate bound-states solution of the Dirac equation with some thermodynamic properties for the deformed Hylleraas plus deformed Woods-Saxon potential, The European Physical Journal Plus, Volume 132 (2017) no. 7 | DOI:10.1140/epjp/i2017-11573-x
Victor A.S.V. Bittencourt; Alex E. Bernardini Entanglement of Dirac bi-spinor states driven by Poincaré classes of SU(2)⊗SU(2) coupling potentials, Annals of Physics, Volume 364 (2016), p. 182 | DOI:10.1016/j.aop.2015.11.004
Avadh Saxena Topological defects and topological materials, Integrated Ferroelectrics, Volume 174 (2016) no. 1, p. 1 | DOI:10.1080/10584587.2016.1189310
L. M. Woods; D. A. R. Dalvit; A. Tkatchenko; P. Rodriguez-Lopez; A. W. Rodriguez; R. Podgornik Materials perspective on Casimir and van der Waals interactions, Reviews of Modern Physics, Volume 88 (2016) no. 4 | DOI:10.1103/revmodphys.88.045003
J. M. Shao; G. W. Yang Photoconductivity in Dirac materials, AIP Advances, Volume 5 (2015) no. 11 | DOI:10.1063/1.4935644
Victor A.S.V. Bittencourt; Salomon S. Mizrahi; Alex E. Bernardini SU(2)⊗SU(2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions, Annals of Physics, Volume 355 (2015), p. 35 | DOI:10.1016/j.aop.2015.02.001
André Eckardt; Egidijus Anisimovas High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective, New Journal of Physics, Volume 17 (2015) no. 9, p. 093039 | DOI:10.1088/1367-2630/17/9/093039
Ivana Vasić; Alexandru Petrescu; Karyn Le Hur; Walter Hofstetter Chiral bosonic phases on the Haldane honeycomb lattice, Physical Review B, Volume 91 (2015) no. 9 | DOI:10.1103/physrevb.91.094502
Björn Sbierski; Emil J. Bergholtz; Piet W. Brouwer Quantum critical exponents for a disordered three-dimensional Weyl node, Physical Review B, Volume 92 (2015) no. 11 | DOI:10.1103/physrevb.92.115145
Laurent Raymond; Alberto D. Verga; Arnaud Demion Anomalous quantum Hall effect induced by disorder in topological insulators, Physical Review B, Volume 92 (2015) no. 7 | DOI:10.1103/physrevb.92.075101
Y. F. Guo; A. J. Princep; X. Zhang; P. Manuel; D. Khalyavin; I. I. Mazin; Y. G. Shi; A. T. Boothroyd Coupling of magnetic order to planar Bi electrons in the anisotropic Dirac metalsAMnBi2 (A =Sr,Ca), Physical Review B, Volume 90 (2014) no. 7 | DOI:10.1103/physrevb.90.075120

Cité par 81 documents. Sources : Crossref

Commentaires - Politique

Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !

Publier un nouveau commentaire:

Publier une nouvelle réponse: