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  • Letter
  • Open Access

Broken symmetry in ideal Chern bands

Hui Liu1, Kang Yang2, Ahmed Abouelkomsan3, Zhao Liu4,5,*, and Emil J. Bergholtz1,†

  • *Contact author: zhaol@zju.edu.cn
  • †Contact author: emil.bergholtz@fysik.su.se
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Phys. Rev. B 111, L201105 – Published 9 May, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L201105

Abstract

Recent observations of the fractional anomalous quantum Hall effect in moiré materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau-level-like single-particle states form an “ideal” Chern band and local interactions lead to Laughlin-like FCIs at 1/3 filling has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and, e.g., at 2/3 filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favored. In fact, even the exact Laughlin-like zero modes at 1/3 filling have a nonuniform density tracking the underlying quantum geometry. Switching to a Coulomb interaction, the ideal Chern band with electron filling of 1/4 features trivial charge density wave states. Moreover, applying a particle-hole transformation reveals that the ideal Chern band with hole filling of 3/4 supports a quantum anomalous Hall crystal with quantized Hall conductance of e2/h. These phenomena have no direct lowest Landau level counterpart.

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Phys. Rev. B 111, L201105– Published 9 May, 2025
  • Received 17 February 2024
  • Revised 12 April 2025
  • Accepted 15 April 2025
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