2024/02/06 by Hui Liu, Liu, Hui, Kang Yang +7 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2402.04303
openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 favoured. In fact, even the exact Laughlin-like zero modes at 1/3 filling have a non-uniform 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.