Higher vortexability: zero field realization of higher Landau levels
arxiv(2024)
摘要
The rise of moiré materials has led to experimental realizations of
integer and fractional Chern insulators in small or vanishing magnetic fields.
At the same time, a set of minimal conditions sufficient to guarantee a Abelian
fractional state in a flat band were identified, namely "ideal" or "vortexable"
quantum geometry. Such vortexable bands share essential features with the
lowest Landau level, while excluding the need for more fine-tuned aspects such
as flat Berry curvature. A natural and important generalization is to ask if
such conditions can be extended to capture the quantum geometry of higher
Landau levels, particularly the first (1LL), where non-Abelian states at ν =
1/2,2/5 are known to be competitive. The possibility of realizing these states
at zero magnetic field , and perhaps even more exotic ones, could become a
reality if we could identify the essential structure of the 1LL in Chern bands.
In this work, we introduce a precise definition of 1LL quantum geometry, along
with a figure of merit that measures how closely a given band approaches the
1LL. We apply the definition to identify two models with 1LL structure – a toy
model of double bilayer twisted graphene and a more realistic model of strained
Bernal graphene.
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