Quarter-filled Kitaev-Hubbard Model: A Quantum Hall State in an Optical Lattice

TL;DR

This paper explores how cold atoms in honeycomb optical lattices with strong interactions and spin-orbit coupling can realize quantum Hall states with chiral edge modes at quarter filling.

Contribution

It demonstrates the existence of quantum Hall states with chiral edge states in a quarter-filled Kitaev-Hubbard model with spin-orbit coupling.

Findings

Chiral edge states exist within a finite parameter range.

Non-zero Chern number bands are realized in the non-interacting limit.

Interactions can preserve quantum Hall states under certain conditions.

Abstract

We analyze the Physics of cold atoms in honeycomb optical lattices with on-site repulsion and spin-orbit couplings that break time reversal symmetry. Such systems, at half filling and large on-site repulsion, have been proposed as a possible realization of the Kitaev model. The spin-orbit couplings break the spin degeneracy and, if strong-enough, lead to four non-overlapping bands in the non-interacting limit. These bands carry non-zero Chern number and therefore the non-interacting system has non-zero angular momentum and chiral edge states at 1/4 and 3/4 filling. We have investigated the effect of interactions using the variational cluster perturbation theory and conclude that the chiral edge states exist in finite range of interaction and hopping parameter space.