Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moir\'e structures

TL;DR

This paper presents a theoretical framework explaining the emergence of fractional quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures, emphasizing the role of electron-electron interactions in forming flat, topologically nontrivial bands.

Contribution

It introduces a microscopic theory showing how electron interactions induce nearly flat Chern-1 bands and FQAH phases in rhombohedral graphene moiré systems, extending to four and six-layer analogs.

Findings

Electron-electron interactions create flat, topologically nontrivial bands.

FQAH phases are linked to filling of valley-polarized Chern-1 bands.

Suitable parameters identified for hosting FQAH in multilayer structures.

Abstract

Remarkable recent experiments on the moir\'e structure formed by pentalayer rhombohedral graphene aligned with a hexagonal Boron-Nitride substrate report the discovery of a zero field fractional quantum hall effect. These "(Fractional) Quantum Anomalous Hall" ((F)QAH) phases occur for one sign of a perpendicular displacement field, and correspond, experimentally, to full or partial filling of a valley polarized Chern-$1$ band. Such a band is absent in the non-interacting band structure. Here we show that electron-electron interactions play a crucial role, and present microscopic theoretical calculations demonstrating the emergence of a nearly flat, isolated, Chern-$1$ band and FQAH phases in this system. We also study the four and six-layer analogs and identify parameters where a nearly flat isolated Chern-$1$ band emerges which may be suitable to host FQAH physics.