Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
arxiv(2024)
摘要
Breakthrough experiments have recently realized fractional Chern insulators
(FCIs) in moiré materials. However, all states observed are Abelian, the
possible existence of more exotic non-Abelian FCIs remains controversial both
experimentally and theoretically. Here, we investigate the competition between
charge density wave order, gapless composite fermion liquids and non-Abelian
Moore-Read states at half-filling of a moiré band. Although groundstate
(quasi-)degeneracies and spectral flow is not sufficient for distinguishing
between charge order and Moore-Read states, we find evidence using entanglement
spectroscopy that both these states of matter can be realized with realistic
Coulomb interactions. In a double twisted bilayer graphene model transitions
between these phases by tuning the coupling strength between the layers: at
weak coupling there is a composite Fermi liquid phase and at strong coupling a
low entanglement state signaling CDW order emerges. Remarkably, however, there
is compelling evidence for a non-Abelian Moore-Read FCI phase at intermediate
coupling.
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