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

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 $\boldsymbolσ$ with momenta $\boldsymbol{p}$ is configured by a material dependent $3\times 3$ matrix $\boldsymbolΛ$ as $σ^μΛ_μ^νp_ν$. We show that the spectra of the interface suggap states depend strongly on the relative choices of $\boldsymbolΛ$ in the two topological insulators. In particular, we focus on properties of gapless states which appear when $\boldsymbolΛ$ 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.

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