Robustness of Gapless Interface State in a Junction of Two Topological Insulators

TL;DR

This paper investigates the stability and characteristics of gapless interface states between two topological insulators with different spin-orbit coupling configurations, emphasizing their robustness under symmetry-breaking perturbations.

Contribution

It introduces a theoretical framework for analyzing subgap states at topological insulator interfaces with different spin-orbit matrices and explores their robustness.

Findings

Gapless states occur when spin-orbit matrices are related by momentum inversion.

The spectra of interface states depend on the relative spin-orbit configurations.

Gapless states show robustness against certain symmetry-breaking perturbations.

Abstract

We theoretically study subgap states appearing at the interface between two three-dimensional topological insulators which have different configurations in the spin-orbit interactions from each other. The coupling of spin $\boldsymbol{\sigma}$ with momenta $\boldsymbol{p}$ is configured by a material dependent $3\times 3$ matrix $\boldsymbol{\Lambda}$ as ${\sigma}^\mu {\Lambda}_\mu^\nu p_\nu$. We show that the spectra of the interface suggap states depend strongly on the relative choices of $\boldsymbol{\Lambda}$ in the two topological insulators. In particular, we focus on properties of gapless states which appear when $\boldsymbol{\Lambda}$ in two topological insulators are connected by the inversion in momentum space. We also discuss the robustness of the gapless states under perturbations breaking the time-reversal symmetry or the band-inversion symmetry by the numerical simulation.