Broken Symmetry in Ideal Chern Bands
arxiv(2024)
摘要
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. Moreover, by switching to a Coulomb
interaction, the ideal Chern band features charge density wave states with no
lowest Landau level counterpart.
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