Thermodynamic and topological phase diagrams of correlated topological insulators

TL;DR

This paper extends the concept of topological invariants to finite temperatures and investigates how electron interactions influence topological insulators, revealing that correlations can suppress nontrivial phases and induce a transition to a Mott insulator.

Contribution

It introduces a framework for defining topological phases of density matrices at finite temperature and analyzes the impact of correlations on topological phases using extended Kane-Mele models.

Findings

Correlation effects suppress nontrivial topological phases

Interaction induces a transition to a trivial Mott insulator

Finite temperature topological invariants are extended to interacting systems

Abstract

A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. Influence of electron interactions on topological insulators at finite temperatures is investigated. A correlated topological insulator is described by the Kane-Mele model, which is extended by the interaction term of the Falicov-Kimball type. Within the Hartree-Fock and the Hubbard I approximations the thermodynamic and topological phase diagrams are determined, where the long-range order is included. The results show that correlation effects lead to a strong suppression of the existence of the nontrivial topological phase. In the homogeneous phase we find a purely-correlation driven phase transition into the topologically trivial Mott insulator.