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

TL;DR

This paper explores the potential realization of non-Abelian fractional Chern insulators in moiré materials, demonstrating evidence for Moore-Read states and their competition with other phases through advanced spectral and entanglement analyses.

Contribution

It provides the first evidence that non-Abelian Moore-Read FCIs can exist in moiré bands, analyzing their properties and phase transitions with Coulomb interactions and layer coupling.

Findings

Evidence for Moore-Read non-Abelian states in moiré bands.

Identification of phase transitions between CFL, CDW, and Moore-Read states.

Observation of mixed Pfaffian and anti-Pfaffian behavior in ground states.

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.