Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two

TL;DR

This paper demonstrates the existence of fractional quantum Hall effects in a topological flat band with Chern number two, using numerical evidence for both bosonic and fermionic systems in a three-band lattice model.

Contribution

It provides the first numerical evidence of fractional quantum Hall states in a C=2 topological flat band in a lattice model.

Findings

Bosonic FQHE at ν=1/3 with three-fold ground state degeneracy

Fermionic FQHE at ν=1/5 with robust gap

Presence of fractional Chern number in ground states

Abstract

Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number C=2. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $\nu=1/3$ filling characterized by three-fold quasi-degeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $\nu=1/5$ filling with short-range interactions.