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Broken Symmetry in Ideal Chern Bands

Published 6 Feb 2024 in cond-mat.str-el and cond-mat.mes-hall | (2402.04303v3)

Abstract: Recent observations of the fractional anomalous quantum Hall effect in moir\'e 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.

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