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 $\mathit{\sigma }$ with momenta $\mathit{p}$ is configured by a material dependent $3\times 3$ matrix $\mathbf{\Lambda }$ 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 $\mathbf{\Lambda }$ in the two topological insulators. In particular, we focus on properties of gapless states which appear when $\mathbf{\Lambda }$ 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.