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arXiv · 2405.08887

Non-Abelian Fractional Chern Insulators and Competing States in Flat Moir\'e Bands

Hui Liu·Zhao Liu·Emil J. Bergholtz
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Abstract

Breakthrough experiments have recently realized fractional Chern insulators (FCIs) in moir\'e 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 (CDW) order, gapless composite fermion liquid (CFL), and non-Abelian Moore-Read states at half-filling of a moir\'e band. Although groundstate (quasi-)degeneracies and spectral flow are 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 Coulomb interactions. By further analyzing the graviton excitations of Moore-Read states, we unveil that the ground states exhibit a mixed behavior of Pfaffian and anti-Pfaffian, despite the weak breaking of particle-hole symmetry. In a double twisted bilayer graphene model, transitions between these phases can be driven by the coupling strength between the layers: at weak coupling there is a CFL phase and at strong coupling a CDW order emerges. Remarkably, however, there is compelling evidence for a non-Abelian Moore-Read FCI phase at intermediate coupling.

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Hui Liu, Zhao Liu, Emil J. Bergholtz. 2024-05-14. Non-Abelian Fractional Chern Insulators and Competing States in Flat Moir\'e Bands. https://doi.org/10.1103/43nq-ntqm

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