Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene

TL;DR

This paper develops a self-consistent Hartree-Fock theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene, providing insights into the stability and convergence of FQAH states.

Contribution

It introduces a unified theoretical framework using charge neutrality scheme and exact diagonalization to analyze FQAH in rhombohedral pentalayer graphene.

Findings

Charge neutrality scheme ensures convergence in Hartree-Fock calculations.

Hartree-Fock band structure supports FQAH state stability.

Exact diagonalization confirms robustness of FQAH states.

Abstract

The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In particular, we focus on the convergence of the Hartree-Fock calculation with various reference fields and discuss the stability of the FQAH states in PLG. We show that the so-called charge neutrality scheme provides an unambiguous result for the Hartree-Fock calculation, as it ensures a convergence with respect to the momentum cutoff. Based on the Hartree-Fock band structure, we further carry out exact diagonalization calculations to explore the stability of the FQAH states in PLG. Our work provides an improved and unified (minimal) theoretical framework to understand the FQAH effect in rhombohedral PLG and paves the way for future experimental and theoretical studies.