Phase structure of 2-dimensional topological insulators by lattice strong coupling expansion

TL;DR

This paper investigates how strong electron-electron interactions alter the phase diagram of 2D topological insulators, revealing a new antiferromagnetic phase between conventional and topological phases using lattice gauge theory techniques.

Contribution

It introduces a strong coupling expansion approach to analyze the phase structure of interacting 2D topological insulators, discovering a novel antiferromagnetic phase.

Findings

Interaction modifies the topological phase structure.

A new antiferromagnetic phase emerges between known phases.

Analogy to Aoki phase in lattice QCD is discussed.

Abstract

The phase structure of 2-dimensional topological insulators under a sufficiently strong electron-electron interaction is investigated. The effective theory is constructed by extending the idea of the Kane-Mele model on the graphenelike honeycomb lattice, in terms of U(1) lattice gauge theory (quantum electrodynamics, QED). We analyze the phase structure by the techniques of strong coupling expansion of lattice gauge theory. As a result, we find that the topological phase structure of the system is modified by the electron-electron interaction. There evolves a new phase with the antiferromagnetism not parallel to the direction pointed by the spin-orbit coupling, in between the conventional and the topological insulator phases. We also discuss the physical implication of the new phase structure found here, in analogy to the parity-broken phase in lattice quantum chromodynamics (QCD), known as "Aoki phase".