Quantum Hall Effects in a Non-Abelian Honeycomb Lattice

TL;DR

This paper investigates tunable quantum Hall effects in a non-Abelian honeycomb optical lattice with multiple Dirac points, revealing how different perturbations induce various quantum Hall states and extending understanding of these effects in complex lattice systems.

Contribution

It introduces the study of quantum Hall effects in a non-Abelian honeycomb lattice with multiple Dirac points, highlighting the effects of perturbations on different quantum Hall phenomena.

Findings

Gauge-field-dressed next-nearest-neighbor hopping induces quantum spin Hall effect.

Zeeman field induces quantum anomalous valley Hall effect.

Multiple quantum Hall states with distinct edge modes are identified.

Abstract

We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall effects in honeycomb optical lattice when the internal valley degrees of freedom enlarge.