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Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model (2403.05522v3)

Published 8 Mar 2024 in cond-mat.str-el and cond-mat.mes-hall

Abstract: We propose a minimal "three-patch model" for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moir\'e potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean field calculations even without a moir\'e potential, enabling a realization of the AHC state. Our model is built upon the dissection of the Brillouin zone into patches centered around high symmetry points. Within this model, the wavefunctions at high symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the non-interacting wavefunctions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

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References (73)
  1. E. Wigner. On the Interaction of Electrons in Metals. Phys. Rev., 46(11):1002–1011, December 1934. Publisher: American Physical Society.
  2. Crystallization of a two-dimensional electron gas in a magnetic field. Soviet Journal of Experimental and Theoretical Physics Letters, 22:11, July 1975. ADS Bibcode: 1975JETPL..22…11L.
  3. Observation of a Magnetically Induced Wigner Solid. Phys. Rev. Lett., 60(26):2765–2768, June 1988. Publisher: American Physical Society.
  4. Observation of a reentrant insulating phase near the 1/3 fractional quantum Hall liquid in a two-dimensional hole system. Phys. Rev. Lett., 68(8):1188–1191, February 1992. Publisher: American Physical Society.
  5. Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions. Nat. Mater., 21(3):311–316, March 2022. Publisher: Nature Publishing Group.
  6. Direct observation of a magnetic field-induced Wigner crystal, December 2023. arXiv:2312.11632 [cond-mat].
  7. C. C. Grimes and G. Adams. Evidence for a Liquid-to-Crystal Phase Transition in a Classical, Two-Dimensional Sheet of Electrons. Phys. Rev. Lett., 42(12):795–798, March 1979. Publisher: American Physical Society.
  8. Wigner Crystallization and Metal-Insulator Transition of Two-Dimensional Holes in GaAs at $B=0$. Phys. Rev. Lett., 82(8):1744–1747, February 1999. Publisher: American Physical Society.
  9. Observation of spontaneous ferromagnetism in a two-dimensional electron system. Proceedings of the National Academy of Sciences, 117(51):32244–32250, December 2020. Publisher: Proceedings of the National Academy of Sciences.
  10. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature, 595(7865):53–57, July 2021. Publisher: Nature Publishing Group.
  11. Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Nature, 595(7865):48–52, July 2021. Publisher: Nature Publishing Group.
  12. Experimental Determination of the Energy per Particle in Partially Filled Landau Levels. Phys. Rev. Lett., 126(15):156802, April 2021. Publisher: American Physical Society.
  13. Observation of an electronic microemulsion phase emerging from a quantum crystal-to-liquid transition, December 2023. arXiv:2311.18069 [cond-mat].
  14. Quantum Melting of a Disordered Wigner Solid, February 2024. arXiv:2402.05456 [cond-mat].
  15. Cooperative ring exchange theory of the fractional quantized Hall effect. Phys. Rev. Lett., 56(8):873–876, February 1986. Publisher: American Physical Society.
  16. Compatibility of Crystalline Order and the Quantized Hall Effect. Phys. Rev. Lett., 57(7):922–922, August 1986. Publisher: American Physical Society.
  17. Cooperative ring exchange and the fractional quantum Hall effect. Phys. Rev. B, 36(3):1620–1646, July 1987. Publisher: American Physical Society.
  18. “Hall crystal” versus Wigner crystal. Phys. Rev. B, 39(12):8525–8551, April 1989. Publisher: American Physical Society.
  19. Fractional quantum anomalous Hall effect in multilayer graphene. Nature, 626(8000):759–764, February 2024. Number: 8000 Publisher: Nature Publishing Group.
  20. N. Regnault and B. Andrei Bernevig. Fractional Chern Insulator. Phys. Rev. X, 1(2):021014, December 2011. Publisher: American Physical Society.
  21. High-Temperature Fractional Quantum Hall States. Phys. Rev. Lett., 106(23):236802, June 2011. Publisher: American Physical Society.
  22. Nearly Flatbands with Nontrivial Topology. Phys. Rev. Lett., 106(23):236803, June 2011. Publisher: American Physical Society.
  23. Fractional Quantum Hall States at Zero Magnetic Field. Phys. Rev. Lett., 106(23):236804, June 2011. Publisher: American Physical Society.
  24. Topological flat band models and fractional chern insulators. Int. J. Mod. Phys. B, 27(24):1330017, September 2013. Publisher: World Scientific Publishing Co.
  25. Recent developments in fractional Chern insulators. In Tapash Chakraborty, editor, Encyclopedia of Condensed Matter Physics (Second Edition), pages 515–538. Academic Press, Oxford, January 2024.
  26. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature, 579(7797):56–61, March 2020. Number: 7797 Publisher: Nature Publishing Group.
  27. Theory of fractional quantum anomalous Hall phases in pentalayer rhombohedral graphene moir\’e structures, November 2023. arXiv:2311.03445 [cond-mat].
  28. Fractional quantum anomalous Hall effects in rhombohedral multilayer graphene in the moir\’eless limit and in Coulomb imprinted superlattice, November 2023. arXiv:2311.04217 [cond-mat].
  29. Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field, November 2023. arXiv:2311.05568 [cond-mat].
  30. Theory of fractional Chern insulator states in pentalayer graphene moir\’e superlattice, December 2023. arXiv:2311.14368 [cond-mat].
  31. Moir\’e Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moir\’e Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices, December 2023. arXiv:2312.11617 [cond-mat].
  32. Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science, 314(5806):1757–1761, December 2006. Publisher: American Association for the Advancement of Science.
  33. Topological insulators with inversion symmetry. Phys. Rev. B, 76(4):045302, July 2007. Publisher: American Physical Society.
  34. Quantum Spin Hall Effect in Inverted Type-II Semiconductors. Phys. Rev. Lett., 100(23):236601, June 2008. Publisher: American Physical Society.
  35. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys, 5(6):438–442, June 2009. Publisher: Nature Publishing Group.
  36. Berry Phase Theory of the Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites. Phys. Rev. Lett., 83(18):3737–3740, November 1999. Publisher: American Physical Society.
  37. Spin anisotropy and quantum Hall effect in the kagom\’e lattice: Chiral spin state based on a ferromagnet. Phys. Rev. B, 62(10):R6065–R6068, September 2000. Publisher: American Physical Society.
  38. Quantized topological Hall effect in skyrmion crystal. Phys. Rev. B, 92(11):115417, September 2015. Publisher: American Physical Society.
  39. Magnetic texture-induced thermal Hall effects. Phys. Rev. B, 87(2):024402, January 2013. Publisher: American Physical Society.
  40. Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers. Phys. Rev. Lett., 122(8):086402, February 2019. Publisher: American Physical Society.
  41. Topological magnetic textures in magnetic topological insulators. Phys. Rev. Res., 3(3):033173, August 2021. Publisher: American Physical Society.
  42. Magnetic skyrmion crystal at a topological insulator surface. Phys. Rev. B, 105(3):035156, January 2022. Publisher: American Physical Society.
  43. The Geometric phase in quantum systems: foundations, mathematical concepts, and applications in molecular and condensed matter physics. Springer, 2003.
  44. John A. Hertz. Quantum critical phenomena. Phys. Rev. B, 14:1165–1184, Aug 1976.
  45. A. J. Millis. Effect of a nonzero temperature on quantum critical points in itinerant fermion systems. Phys. Rev. B, 48:7183–7196, Sep 1993.
  46. Superconductivity from weak repulsion in hexagonal lattice systems. Phys. Rev. B, 89:144501, Apr 2014.
  47. Spin-fermion model near the quantum critical point: One-loop renormalization group results. Phys. Rev. Lett., 84:5608–5611, Jun 2000.
  48. Ar. Abanov and A. Chubukov. Anomalous scaling at the quantum critical point in itinerant antiferromagnets. Phys. Rev. Lett., 93:255702, Dec 2004.
  49. Quantum phase transitions of metals in two spatial dimensions. ii. spin density wave order. Phys. Rev. B, 82:075128, Aug 2010.
  50. Renormalization group analysis of a fermionic hot-spot model. Phys. Rev. B, 90:104505, Sep 2014.
  51. H. J. Schulz. Superconductivity and antiferromagnetism in the two-dimensional hubbard model: Scaling theory. Europhysics Letters, 4(5):609, sep 1987.
  52. I. E. Dzialoshinskii. The superconducting transitions due to Van Hove singularities in the electron spectrum. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, 93:1487–1498, October 1987.
  53. Antiferromagnetism and superconductivity in a quasi two-dimensional electron gas. scaling theory of a generic hubbard model. J. Phys. France, 48(10):1613–1618, 1987.
  54. Truncation of a two-dimensional fermi surface due to quasiparticle gap formation at the saddle points. Phys. Rev. Lett., 81:3195–3198, Oct 1998.
  55. Superconductivity close to the mott state: From condensed-matter systems to superfluidity in optical lattices. Annals of Physics, 324(7):1452–1515, 2009. July 2009 Special Issue.
  56. Chiral superconductivity from repulsive interactions in doped graphene. Nature Physics, 8(2):158–163, Feb 2012.
  57. Unconventional superconductivity and density waves in twisted bilayer graphene. Phys. Rev. X, 8:041041, Dec 2018.
  58. Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis. Phys. Rev. B, 106:155115, Oct 2022.
  59. Quantized response and topology of magnetic insulators with inversion symmetry. Phys. Rev. B, 85(16):165120, April 2012. Publisher: American Physical Society.
  60. Bulk topological invariants in noninteracting point group symmetric insulators. Phys. Rev. B, 86(11):115112, September 2012. Publisher: American Physical Society.
  61. Symmetry-based indicators of band topology in the 230 space groups. Nat Commun, 8(1):50, June 2017. Number: 1 Publisher: Nature Publishing Group.
  62. Topological quantum chemistry. Nature, 547(7663):298–305, July 2017. Number: 7663 Publisher: Nature Publishing Group.
  63. Hoi Chun Po. Symmetry indicators of band topology. J. Phys.: Condens. Matter, 32(26):263001, April 2020. Publisher: IOP Publishing.
  64. Band Representations and Topological Quantum Chemistry. Annual Review of Condensed Matter Physics, 12(1):225–246, 2021. _eprint: https://doi.org/10.1146/annurev-conmatphys-041720-124134.
  65. Band structure of A B C -stacked graphene trilayers. Phys. Rev. B, 82(3):035409, July 2010.
  66. Ab initio theory of moiré superlattice bands in layered two-dimensional materials. Phys. Rev. B, 89(20):205414, May 2014.
  67. Electronic properties of graphene/hexagonal-boron-nitride moiré superlattice. Phys. Rev. B, 90(15):155406, October 2014.
  68. Nearly flat Chern bands in moir\’e superlattices. Phys. Rev. B, 99(7):075127, February 2019. Publisher: American Physical Society.
  69. Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moire superlattices, April 2023. arXiv:2304.12874 [cond-mat].
  70. Density functional investigation of rhombohedral stacks of graphene: Topological surface states, nonlinear dielectric response, and bulk limit. Phys. Rev. B, 84(16):165404, October 2011. Publisher: American Physical Society.
  71. Solitons in Polyacetylene. Phys. Rev. Lett., 42(25):1698–1701, June 1979. Publisher: American Physical Society.
  72. Half- and quarter-metals in rhombohedral trilayer graphene. Nature, 598(7881):429–433, October 2021. Number: 7881 Publisher: Nature Publishing Group.
  73. Sublattice structure and topology in spontaneously crystallized electronic states, February 2024. arXiv:2402.17867 [cond-mat].
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