Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field

TL;DR

This paper explores the emergence and stability of fractional quantum anomalous Hall effects in rhombohedral multilayer graphene under strong displacement fields, combining theoretical models and numerical methods.

Contribution

It introduces a comprehensive interacting model for RnG and demonstrates the universality and stability of FQAH and IQAH phases across multiple layer configurations.

Findings

FQAH phase is stable in RnG with varying displacement fields

The stability of FQAH depends on the number of layers n

Both IQAH and FQAH are theoretically universal in RnG

Abstract

We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the noninteracting continuum model and the many-body Coulomb interaction. We then discuss the integer quantum anomalous Hall (IQAH) effect in RnG and the role of the Hartree-Fock approach in understanding its appearance. Next, we explore the FQAH effect in RnG for $n=3$--$6$ using a combination of constrained Hartree-Fock and exact diagonalization methods. We characterize the stability of the FQAH phase by the size of the FQAH gap and find that RnG generally has a stable FQAH phase, although the required displacement field varies significantly among different $n$ values. Our work establishes the theoretical universality of both IQAH and FQAH in RnG.