Quantum Hall and Light Responses in a 2D Topological Semimetal

Karyn Le Hur; Sariah Al Saati

doi:10.5802/crphys.202

Article de recherche

Quantum Hall and Light Responses in a 2D Topological Semimetal
[Réponses de Hall quantique et à la lumière dans un semimétal topologique à 2D]

Karyn Le Hur ¹ ; Sariah Al Saati ¹

¹ CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, France

Comptes Rendus. Physique, Volume 25 (2024), pp. 415-432.

Résumé
Abstract

Nous avons récemment introduit en théorie un semimétal topologiquement protégé dans un plan de graphène qui présente un mode d’énergie nulle robuste aux interactions et au désordre. Nous adressons ici les caractéristiques de transport et la réponse à la lumière résonante polarisée circulairement de ce semimétal résolue aux points de Dirac. Nous montrons que la conductivité de Hall de la bande du bas est topologique et révèle un invariant $ℤ$ qui est mesuré par la lumière. Nous montrons aussi que la conductivité de Hall associée aux bandes intermédiaires peut être évaluée rigoureusement en présence d’un croisement de bandes, incluant la surface de Fermi, et introduisons l’existence d’un invariant topologique $ℤ$ ₂ associé. Nous élaborons sur la correspondance avec la physique des états de bords comme un demi-métal topologique protégé i.e. une des populations de spin polarisée dans le plan est dans une phase isolante en relation avec le mode d’énergie nulle dans le spectre d’énergie alors que l’autre population de spin est dans un régime métallique. Le transport quantifié aux bords du système est aussi équivalent à une demi-conductance pour les populations de spin le long de la direction z. Nous formulons un parallèle entre la réponse de Hall topologique et une paire de nombres topologiques ½ correspondant à une paire de ½-Skyrmions à travers l’étude de la réponse de la lumière résolue dans l’espace réciproque et sur la sphère.

We have recently identified a protected topological semimetal in graphene which presents a zero-energy edge mode robust to disorder and interactions. Here, we address the characteristics of this semimetal and show that the $ℤ$ topological invariant of the Hall conductivity associated to the lowest energy band can be equivalently measured from the resonant response to circularly polarized light resolved at the Dirac points. The (non-quantized) conductivity responses of the intermediate energy bands, including the Fermi surface, also give rise to a $ℤ$ ₂ invariant. We emphasize on the bulk-edge correspondence as a protected topological half metal, i.e. one spin-population polarized in the plane is in the insulating phase related to the robust edge mode while the other is in the metallic regime. The quantized transport at the edges is equivalent to a $\frac{1}{2} - \frac{1}{2}$ conductance for spin polarizations along z direction. We also build a parallel between the topological Hall response and a pair of half numbers (half Skyrmions) through the light response locally resolved in momentum space and on the sphere.

Reçu le : 2024-04-23
Révisé le : 2024-07-18
Accepté le : 2024-09-04
Publié le : 2024-12-05

DOI : 10.5802/crphys.202

Keywords: Topological systems, Semimetals, Hall conductivity, Response to circular light
Mots-clés : Systèmes Topologiques, Semimétaux, Conductivité de Hall, Réponse à la lumière circulaire

Affiliations des auteurs :

Karyn Le Hur ¹ ; Sariah Al Saati ¹

¹ CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRPHYS_2024__25_G1_415_0,
     author = {Karyn Le Hur and Sariah Al Saati},
     title = {Quantum {Hall} and {Light} {Responses} in a {2D} {Topological} {Semimetal}},
     journal = {Comptes Rendus. Physique},
     pages = {415--432},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {25},
     year = {2024},
     doi = {10.5802/crphys.202},
     language = {en},
}

TY  - JOUR
AU  - Karyn Le Hur
AU  - Sariah Al Saati
TI  - Quantum Hall and Light Responses in a 2D Topological Semimetal
JO  - Comptes Rendus. Physique
PY  - 2024
SP  - 415
EP  - 432
VL  - 25
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.202
LA  - en
ID  - CRPHYS_2024__25_G1_415_0
ER  -

%0 Journal Article
%A Karyn Le Hur
%A Sariah Al Saati
%T Quantum Hall and Light Responses in a 2D Topological Semimetal
%J Comptes Rendus. Physique
%D 2024
%P 415-432
%V 25
%I Académie des sciences, Paris
%R 10.5802/crphys.202
%G en
%F CRPHYS_2024__25_G1_415_0

Karyn Le Hur; Sariah Al Saati. Quantum Hall and Light Responses in a 2D Topological Semimetal. Comptes Rendus. Physique, Volume 25 (2024), pp. 415-432. doi : 10.5802/crphys.202. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.202/

Bibliographie
Cité par

[1] 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 (1982) no. 6, pp. 405-408 | DOI

[2] M. Kohmoto Topological Invariant and the Quantization of the Hall Conductance, Ann. Phys., Volume 160 (1985) no. 2, pp. 343-354 | DOI

[3] D. T. Tran; A. Dauphin; A. G. Grushin; P. Zoller; N. Goldman Probing topology by ‘heating’: Quantized circular dichroism in ultracold atoms, Sci. adv., Volume 3 (2017), e1701207 | DOI

[4] L. Asteria; D. T. Tran; T. Ozawa et al. Measuring quantized circular dichroism in ultracold topological matter, Nat. Phys., Volume 15 (2019), pp. 449-454 | DOI

[5] P. W. Klein; A. G. Grushin; K. Le Hur Interacting Stochastic Topology and Mott Transition from Light Response, Phys. Rev. B, Volume 103 (2021), 035114 | DOI

[6] K. Le Hur Global and local topological quantized responses from geometry, light, and time, Phys. Rev. B, Volume 105 (2022), 125106 | DOI

[7] J. Legendre; K. Le Hur Spectroscopy and topological properties of a Haldane light system, Phys. Rev. A, Volume 109 (2024), L021701 | DOI

[8] Michel Dyakonov; V. Perel Possibility of Orienting Electron Spins with Current, Sov. Phys. JETP, Volume 13 (1971), p. 467

[9] S. Murakami; N. Nagaosa; S.-C. Zhang Dissipationless Quantum Spin Current at Room Temperature, Science, Volume 301 (2003) no. 5638, pp. 1348-1351 | DOI

[10] C. L. Kane; E. J. Mele Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett., Volume 95 (2005) no. 22, 226801 | DOI

[11] C. L. Kane; E. J. Mele $Z_{2}$ Topological Order and the Quantum Spin Hall Effect, Phys. Rev. Lett., Volume 95 (2005) no. 14, 146802 | DOI

[12] S. Rachel; K. Le Hur Topological insulators and Mott physics from the Hubbard interaction, Phys. Rev. B, Volume 82 (2010), 075106 | DOI

[13] W. Wu; S. Rachel; W.-M. Liu; K. Le Hur Quantum Spin Hall Insulators with Interactions and Lattice Anisotropy, Phys. Rev. B, Volume 85 (2012), 205102 | DOI

[14] M. Hohenadler; T. C. Lang; F. F. Assaad Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study, Phys. Rev. B, Volume 106 (2011), 100403 | DOI

[15] B. A. Bernevig; S.-C. Zhang Quantum Spin Hall Effect, Phys. Rev. Lett., Volume 96 (2006) no. 10, 106802 | DOI

[16] L. Sheng; D. N. Sheng; C. S Ting; F. D. M. Haldane Nondissipative Spin Hall Effect via Quantized Edge Transport, Phys. Rev. Lett., Volume 95 (2005), 136602 | DOI

[17] L. Fu; C. L. Kane Topological insulators with inversion symmetry, Phys. Rev. B, Volume 76 (2007), 045302 | DOI

[18] K. Le Hur; S. Al Saati Topological nodal ring semimetal in graphene, Phys. Rev. B, Volume 107 (2023) no. 16, 165407 | DOI

[19] J. Hutchinson; P. W. Klein; K. Le Hur Analytical approach for the Mott transition in the Kane–Mele–Hubbard model, Phys. Rev. B, Volume 104 (2021), 075120 | DOI

[20] I. Titvinidze; J. Legendre; K. Le Hur; W. Hofstetter Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling, Phys. Rev. B, Volume 105 (2022), 235102 | DOI

[21] F. D. M. Haldane Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property, Phys. Rev. Lett., Volume 93 (2004) no. 20, 206602 | DOI

[22] J. Hutchinson; K. Le Hur Quantum entangled fractional topology and curvatures, Commun. Phys., Volume 4 (2021) no. 1, 144 | DOI

[23] K. Le Hur One-Half Topological Number in Entangled Quantum Physics, Phys. Rev. B, Volume 108 (2023), 235144 | DOI

[24] 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) no. 18, pp. 2015-2018 | DOI

[25] G. W. Semenoff Condensed-Matter Simulation of a Three-Dimensional Anomaly, Phys. Rev. Lett., Volume 53 (1984) no. 26, pp. 2449-2452 | DOI

[26] K. Le Hur Interacting topological quantum aspects with light and geometrical functions, Phys. Rep., Volume 1104 (2025), pp. 1-42 (see also arXiv:2209.15381, 108 pages) | DOI

[27] J. W. McIver; B. Schulte; F.-U. Stein; T. Matsuyama; G. Jotzu; G. Meier; A. Cavalleri Light-induced anomalous Hall effect in graphene, Nat. Phys., Volume 16 (2020), pp. 38-41 | DOI

[28] P. Cheng; P. W. Klein; K. Plekhanov; K. Sengstock; M. Aidelsburger; C. Weitenberg; K. Le Hur Topological proximity effects in a Haldane graphene bilayer system, Phys. Rev. B, Volume 100 (2019), 081107 | DOI

[29] J.-H. Zheng; W. Hofstetter Topological invariant for two-dimensional open systems, Phys. Rev. B, Volume 19 (2018), 195434 | DOI

[30] T. H. Hsieh; H. Ishizuka; L. Balents; T. Hughes Bulk Topological Proximity Effect, Phys. Rev. Lett., Volume 116 (2016), 086802 | DOI

[31] T. Shoman; A. Takayama; T. Sato; S. Souma; T. Takahashi; T. Oguchi; K. Segawa; Y. Ando Topological proximity effect in a topological insulator hybrid, Nat. Commun., Volume 6 (2015), 6547 | DOI

[32] Z. Wang; D.-K. Ki; H. Chen; H. Berger; A. H. MacDonald; A. F. Morpurgo Strong interface-induced spin-orbit interaction in graphene on WS $_{2}$ , Nat. Commun., Volume 6 (2015) no. 1, 8339 | DOI

[33] P. Tiwari; S. K. Srivastav; S. Ray; T. Das; A. Bid Observation of Time-Reversal Invariant Helical Edge-Modes in Bilayer Graphene/WSe $_{2}$ Heterostructure, ACS Nano, Volume 15 (2020) no. 1, pp. 916-922 | DOI

[34] M. Masseroni; M. Gull; A. Panigrahi et al. Spin-orbit proximity in MoS $_{2}$ /bilayer graphene heterostructures, Nat. Commun., Volume 15 (2024), 9251 | DOI

[35] C.-Z. Chang; C.-X. Liu; A. H. MacDonald Colloquium: Quantum anomalous Hall effect, Rev. Mod. Phys., Volume 95 (2023) no. 4, 011002 | DOI

[36] M. V. Berry Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond., Ser. A, Volume 392 (1984) no. 1802, pp. 45-57 | DOI

[37] J. Cayssol Introduction to Dirac materials and topological insulators, Comptes Rendus. Physique, Volume 14 (2013), pp. 760-778 | DOI

[38] S. Matsuura; S. Ryu Momentum space metric, nonlocal operator, and topological insulators, Phys. Rev. B, Volume 82 (2010), 245113 | DOI

[39] L. Henriet; A. Sclocchi; P. P. Orth; K. Le Hur Topology of a dissipative spin: dynamical Chern number, bath induced non-adiabaticity and a quantum dynamo effect, Phys. Rev. B, Volume 95 (2017), 054307 | DOI

[40] C. Repellin; N. Goldman Detecting Fractional Chern Insulators through Circular Dichroism, Phys. Rev. Lett., Volume 122 (2019), 166801 | DOI

[41] F. del Pozo; L. Herviou; K. Le Hur Fractional Topology in Interacting 1D Superconductors, Phys. Rev. B, Volume 107 (2023), 155134 | DOI

[42] E. Bernhardt; B. Chung Hang Cheung; K. Le Hur Majorana fermions and quantum information with fractional topology and disorder, Physical Rev. Research, Volume 5 (2024), 023221 | DOI

[43] R. Shankar; H. Mathur Thomas Precession, Berry potential and the Meron, Phys. Rev. Lett., Volume 73 (1994) no. 14, pp. 1565-1569 | DOI

Cité par Sources :

Commentaires - Politique