A study on correlation effects in two dimensional topological insulators

TL;DR

This paper explores how electron interactions influence finite size effects, phase transitions, and edge state properties in two-dimensional topological insulators, revealing that interactions weaken edge localization but do not induce edge Mott insulators.

Contribution

It provides a detailed analysis of correlation effects in finite size 2D topological insulators using bosonization and inhomogeneous DMFT, highlighting the robustness of the topological phase against interactions.

Findings

Finite size gaps are renormalized by weak interactions.

Edge states remain topologically protected up to a critical interaction strength.

Strong interactions lead to a homogeneous Mott insulator without edge Mott states.

Abstract

We investigate correlation effects in two dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible inter-edge Umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore, the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for "edge Mott insulating states" and the system stays in the topological insulating state, which is adiabatically connected to the non-interacting state, for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.