Spin texture and mirror Chern number in Hg-based chalcogenides

One important feature of surface states in topological insulators is the so-called spin-momentum locking, which means that electron spin is oriented along a fixed direction for a given momentum and forms a texture in the momentum space. In this work, we study spin textures of two typical topological insulators in Hg-based chalcogenides, namely, HgTe and HgS, based on both the first-principles calculation and the eight-band Kane model. We find opposite helicities of spin textures between these two materials, originating from the opposite signs of spin-orbit couplings. Based on the effective Kane model, we present a physical picture to understand opposite spin textures in these two materials with the help of the relationship between spin textures and mirror Chern numbers. We also reveal the existence of gapless states at the interface between HgTe and HgS due to the opposite spin textures and opposite mirror Chern numbers.