High-temperature fractional quantum Hall state in the Floquet kagome flat band

Liu, Hang; Sethi, Gurjyot; Sheng, D. N.; Zhou, Yinong; Sun, Jia-Tao; Meng, Sheng; Liu, Feng

doi:10.1103/physrevb.105.l161108

Title: High-temperature fractional quantum Hall state in the Floquet kagome flat band

Journal Article · 29 April 2022 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.105.l161108 · OSTI ID:1905826

Liu, Hang ^[1];

^[2]; Sheng, D. N. ^[3]; Zhou, Yinong ^[2]; Sun, Jia-Tao ^[4]; Meng, Sheng ^[5];

^[2]

Chinese Academy of Sciences (CAS), Beijing (China); Univ. of Utah, Salt Lake City, UT (United States); Songshan Lake Materials Laboratory, Guangdong (China)
Univ. of Utah, Salt Lake City, UT (United States)
California State University, Northridge (CSUN), CA (United States)
Chinese Academy of Sciences (CAS), Beijing (China); Beijing Institute of Technology (China)
Univ. of Utah, Salt Lake City, UT (United States); Songshan Lake Materials Laboratory, Guangdong (China)

A fractional quantum Hall effect (FQHE) has been predicted in a topological flat band (FB) by a single-particle band structure combined with phenomenological theory or solution of a many-body lattice Hamiltonian with fuzzy parameters. A long-standing roadblock toward the realization of a FB-FQHE is lacking the many-body solution of specific materials under realistic conditions. Here, we demonstrate a combined study of single-particle Floquet band theory with exact diagonalization (ED) of a many-body Hamiltonian. We show that a time-periodic circularly polarized laser inverts the sign of second-nearest-neighbor hopping in a kagome lattice and enhances spin-orbit coupling in one spin channel to produce a Floquet FB with a high flatness ratio of bandwidth over band gap, as exemplified in monolayer Pt₃C₃₆S₁₂H₁₂. The ED of the resultant Floquet-kagome lattice Hamiltonian gives a one-third-filling ground state with a laser-dependent excitation gap of a FQH state, up to an estimated temperature above 70 K. Our findings pave the way for exploring the alluding high-temperature FB-FQHE.

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Research Organization:: Univ. of Utah, Salt Lake City, UT (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Key Research and Development Program of China; National Basic Research Program of China; National Natural Science Foundation of China (NSFC); Chinese Academy of Sciences; China Postdoctoral Science Foundation; Guangdong Basic and Applied Basic Research Foundation; China Scholarship Council

Grant/Contract Number:: FG02-04ER46148; FG02-06ER46305; 2020YFA0308800; 2016YFA0300902; 2015CB921001; 91850120; 11774396; 11974045; 12147136; XDB30000000; 2021M700163; 2021A1515110466

OSTI ID:: 1905826

Journal Information:: Physical Review. B, Vol. 105, Issue 16; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (62)

Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance Klitzing, K. v.; Dorda, G.; Pepper, M. Physical Review Letters, Vol. 45, Issue 6 https://doi.org/10.1103/PhysRevLett.45.494	journal	August 1980
s d 2 Graphene: Kagome Band in a Hexagonal Lattice Zhou, Miao; Liu, Zheng; Ming, Wenmei Physical Review Letters, Vol. 113, Issue 23 https://doi.org/10.1103/PhysRevLett.113.236802	journal	December 2014
Ground State of Two-Dimensional Electrons in Strong Magnetic Fields and 1 3 Quantized Hall Effect Yoshioka, D.; Halperin, B. I.; Lee, P. A. Physical Review Letters, Vol. 50, Issue 16 https://doi.org/10.1103/PhysRevLett.50.1219	journal	April 1983
Floquet Fractional Chern Insulators Grushin, Adolfo G.; Gómez-León, Álvaro; Neupert, Titus Physical Review Letters, Vol. 112, Issue 15 https://doi.org/10.1103/PhysRevLett.112.156801	journal	April 2014
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States Haldane, F. D. M. Physical Review Letters, Vol. 51, Issue 7 https://doi.org/10.1103/PhysRevLett.51.605	journal	August 1983
Monte Carlo evaluation of trial wavefunctions for the fractional quantized Hall effect: Spherical geometry Morf, R.; Halperin, B. I. Zeitschrift f�r Physik B Condensed Matter, Vol. 68, Issue 2-3 https://doi.org/10.1007/BF01304256	journal	June 1987
Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering Bukov, Marin; D'Alessio, Luca; Polkovnikov, Anatoli Advances in Physics, Vol. 64, Issue 2 https://doi.org/10.1080/00018732.2015.1055918	journal	March 2015
First-principles design of a half-filled flat band of the kagome lattice in two-dimensional metal-organic frameworks Yamada, Masahiko G.; Soejima, Tomohiro; Tsuji, Naoto Physical Review B, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevB.94.081102	journal	August 2016
Ferromagnetism in the Hubbard model with topological/non-topological flat bands Katsura, Hosho; Maruyama, Isao; Tanaka, Akinori EPL (Europhysics Letters), Vol. 91, Issue 5 https://doi.org/10.1209/0295-5075/91/57007	journal	September 2010
Realization of flat band with possible nontrivial topology in electronic Kagome lattice Li, Zhi; Zhuang, Jincheng; Wang, Li Science Advances, Vol. 4, Issue 11 https://doi.org/10.1126/sciadv.aau4511	journal	November 2018
Zoology of fractional Chern insulators Wu, Yang-Le; Bernevig, B. Andrei; Regnault, N. Physical Review B, Vol. 85, Issue 7 https://doi.org/10.1103/PhysRevB.85.075116	journal	February 2012
Valley-selective optical Stark effect in monolayer WS2 Sie, Edbert J.; McIver, James W.; Lee, Yi-Hsien Nature Materials, Vol. 14, Issue 3 https://doi.org/10.1038/nmat4156	journal	December 2014
Photoinduced Nonequilibrium Topological States in Strained Black Phosphorus Liu, Hang; Sun, Jia-Tao; Cheng, Cai Physical Review Letters, Vol. 120, Issue 23 https://doi.org/10.1103/PhysRevLett.120.237403	journal	June 2018
Band structure engineering of ideal fractional Chern insulators Lee, Ching Hua; Claassen, Martin; Thomale, Ronny Physical Review B, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevB.96.165150	journal	October 2017
Floquet Engineering of Quantum Materials Oka, Takashi; Kitamura, Sota Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031218-013423	journal	March 2019
Quadratic band touching points and flat bands in two-dimensional topological Floquet systems Du, Liang; Zhou, Xiaoting; Fiete, Gregory A. Physical Review B, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevB.95.035136	journal	January 2017
Exotic electronic states in the world of flat bands: From theory to material Liu, Zheng; Liu, Feng; Wu, Yong-Shi Chinese Physics B, Vol. 23, Issue 7 https://doi.org/10.1088/1674-1056/23/7/077308	journal	July 2014
Large, valley-exclusive Bloch-Siegert shift in monolayer WS ₂ Sie, Edbert J.; Lui, Chun Hung; Lee, Yi-Hsien Science, Vol. 355, Issue 6329 https://doi.org/10.1126/science.aal2241	journal	March 2017
Exotic fractional topological states in a two-dimensional organometallic material Li, Wei; Liu, Zheng; Wu, Yong-Shi Physical Review B, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevB.89.125411	journal	March 2014
Screening Magnetic Two-Dimensional Atomic Crystals with Nontrivial Electronic Topology Liu, Hang; Sun, Jia-Tao; Liu, Miao The Journal of Physical Chemistry Letters, Vol. 9, Issue 23 https://doi.org/10.1021/acs.jpclett.8b02783	journal	November 2018
Light-induced anomalous Hall effect in graphene McIver, J. W.; Schulte, B.; Stein, F. -U. Nature Physics, Vol. 16, Issue 1 https://doi.org/10.1038/s41567-019-0698-y	journal	November 2019
Formation of quantum spin Hall state on Si surface and energy gap scaling with strength of spin orbit coupling Zhou, Miao; Ming, Wenmei; Liu, Zheng Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep07102	journal	November 2014
Fractional Chern Insulator Regnault, N.; Bernevig, B. Andrei Physical Review X, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevX.1.021014	journal	December 2011
Topological insulator on the kagome lattice Guo, H. -M.; Franz, M. Physical Review B, Vol. 80, Issue 11 https://doi.org/10.1103/PhysRevB.80.113102	journal	September 2009
Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons Roman-Taboada, Pedro; Naumis, Gerardo G. Physical Review B, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevB.95.115440	journal	March 2017
Fractional Quantum Hall States at Zero Magnetic Field Neupert, Titus; Santos, Luiz; Chamon, Claudio Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236804	journal	June 2011
Light-Induced Type-II Band Inversion and Quantum Anomalous Hall State in Monolayer FeSe Wang, Z. F.; Liu, Zhao; Yang, Jinlong Physical Review Letters, Vol. 120, Issue 15 https://doi.org/10.1103/PhysRevLett.120.156406	journal	April 2018
Two-Dimensional Magnetotransport in the Extreme Quantum Limit Tsui, D. C.; Stormer, H. L.; Gossard, A. C. Physical Review Letters, Vol. 48, Issue 22 https://doi.org/10.1103/PhysRevLett.48.1559	journal	May 1982
High-Temperature Fractional Quantum Hall States Tang, Evelyn; Mei, Jia-Wei; Wen, Xiao-Gang Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236802	journal	June 2011
Nearly Flatbands with Nontrivial Topology Sun, Kai; Gu, Zhengcheng; Katsura, Hosho Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236803	journal	June 2011
Engineering Dirac states in graphene: Coexisting type-I and type-II Floquet-Dirac fermions Liu, Hang; Sun, Jia-Tao; Meng, Sheng Physical Review B, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevB.99.075121	journal	February 2019
Extracting Excitations from Model State Entanglement Sterdyniak, A.; Regnault, N.; Bernevig, B. A. Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.100405	journal	March 2011
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevLett.50.1395	journal	May 1983
Flat Chern Band in a Two-Dimensional Organometallic Framework Liu, Zheng; Wang, Zheng-Fei; Mei, Jia-Wei Physical Review Letters, Vol. 110, Issue 10 https://doi.org/10.1103/PhysRevLett.110.106804	journal	March 2013
Tunable Weyl Points in Periodically Driven Nodal Line Semimetals Yan, Zhongbo; Wang, Zhong Physical Review Letters, Vol. 117, Issue 8 https://doi.org/10.1103/PhysRevLett.117.087402	journal	August 2016
The quantized Hall effect von Klitzing, Klaus Reviews of Modern Physics, Vol. 58, Issue 3 https://doi.org/10.1103/RevModPhys.58.519	journal	July 1986
Observation of Floquet-Bloch States on the Surface of a Topological Insulator Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P. Science, Vol. 342, Issue 6157, p. 453-457 https://doi.org/10.1126/science.1239834	journal	October 2013
Tunable topological states in electron-doped HTT-Pt Zhang, Xiaoming; Wang, Zhenhai; Zhao, Mingwen Physical Review B, Vol. 93, Issue 16 https://doi.org/10.1103/PhysRevB.93.165401	journal	April 2016
Selective scattering between Floquet–Bloch and Volkov states in a topological insulator Mahmood, Fahad; Chan, Ching-Kit; Alpichshev, Zhanybek Nature Physics, Vol. 12, Issue 4 https://doi.org/10.1038/nphys3609	journal	January 2016
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator Chang, C. -Z.; Zhang, J.; Feng, X. Science, Vol. 340, Issue 6129 https://doi.org/10.1126/science.1234414	journal	March 2013
Quantum Anomalous Hall Effect in Hg 1 − y Mn y Te Quantum Wells Liu, Chao-Xing; Qi, Xiao-Liang; Dai, Xi Physical Review Letters, Vol. 101, Issue 14 https://doi.org/10.1103/PhysRevLett.101.146802	journal	October 2008
Photovoltaic Hall effect in graphene Oka, Takashi; Aoki, Hideo Physical Review B, Vol. 79, Issue 8 https://doi.org/10.1103/PhysRevB.79.081406	journal	February 2009
Quantized Hall conductance as a topological invariant Niu, Qian; Thouless, D. J.; Wu, Yong-Shi Physical Review B, Vol. 31, Issue 6 https://doi.org/10.1103/PhysRevB.31.3372	journal	March 1985
Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials Hübener, Hannes; Sentef, Michael A.; De Giovannini, Umberto Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms13940	journal	January 2017
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Large-Area, Free-Standing, Two-Dimensional Supramolecular Polymer Single-Layer Sheets for Highly Efficient Electrocatalytic Hydrogen Evolution Dong, Renhao; Pfeffermann, Martin; Liang, Haiwei Angewandte Chemie International Edition, Vol. 54, Issue 41 https://doi.org/10.1002/anie.201506048	journal	August 2015
Intrinsic Two-Dimensional Organic Topological Insulators in Metal–Dicyanoanthracene Lattices Zhang, L. Z.; Wang, Z. F.; Huang, B. Nano Letters, Vol. 16, Issue 3 https://doi.org/10.1021/acs.nanolett.6b00110	journal	February 2016
Theory of Floquet band formation and local pseudospin textures in pump-probe photoemission of graphene Sentef, M. A.; Claassen, M.; Kemper, A. F. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8047	journal	May 2015
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Topological flat band Models and Fractional Chern Insulators Bergholtz, Emil J.; Liu, Zhao International Journal of Modern Physics B, Vol. 27, Issue 24 https://doi.org/10.1142/S021797921330017X	journal	September 2013
Electron States of 2D Metal–Organic and Covalent–Organic Honeycomb Frameworks: Ab Initio Results and a General Fitting Hamiltonian Silveira, Orlando J.; Alexandre, Simone S.; Chacham, Helio The Journal of Physical Chemistry C, Vol. 120, Issue 35 https://doi.org/10.1021/acs.jpcc.6b05081	journal	August 2016
Theoretical Description of Time-Resolved Photoemission Spectroscopy: Application to Pump-Probe Experiments Freericks, J. K.; Krishnamurthy, H. R.; Pruschke, Th. Physical Review Letters, Vol. 102, Issue 13 https://doi.org/10.1103/PhysRevLett.102.136401	journal	March 2009
Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels Kitagawa, Takuya; Oka, Takashi; Brataas, Arne Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235108	journal	December 2011
Robust half-metallicity and topological aspects in two-dimensional Cu-TPyB Zhang, Xiaoming; Zhao, Mingwen Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep14098	journal	September 2015
Quantized Hall conductivity in two dimensions Laughlin, R. B. Physical Review B, Vol. 23, Issue 10 https://doi.org/10.1103/PhysRevB.23.5632	journal	May 1981
Quantitative experimental test for the theoretical gap energies in the fractional quantum Hall effect Willett, R. L.; Stormer, H. L.; Tsui, D. C. Physical Review B, Vol. 37, Issue 14 https://doi.org/10.1103/PhysRevB.37.8476	journal	May 1988
Prediction of a Two-Dimensional Organic Topological Insulator Wang, Z. F.; Su, Ninghai; Liu, Feng Nano Letters, Vol. 13, Issue 6, p. 2842-2845 https://doi.org/10.1021/nl401147u	journal	May 2013
Quantized Anomalous Hall Effect in Magnetic Topological Insulators Yu, R.; Zhang, W.; Zhang, H. -J. Science, Vol. 329, Issue 5987 https://doi.org/10.1126/science.1187485	journal	June 2010
Fractional quantum Hall effect in the absence of Landau levels Sheng, D. N.; Gu, Zheng-Cheng; Sun, Kai Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1380	journal	July 2011
‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle Haldane, F. D. M. Physical Review Letters, Vol. 67, Issue 8 https://doi.org/10.1103/PhysRevLett.67.937	journal	August 1991
Dirac cones, Floquet side bands, and theory of time-resolved angle-resolved photoemission Farrell, Aaron; Arsenault, A.; Pereg-Barnea, T. Physical Review B, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevB.94.155304	journal	October 2016