Surface-state spin textures in strained bulk HgTe: Strain-induced topological phase transitions

The opening of a band gap due to compressive uniaxial strain renders bulk HgTe a strong three-dimensional topological insulator with protected gapless surface states at any surface. By employing a six-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model, we determine the spin textures of the topological surface states of bulk HgTe uniaxially strained along the $(100)$ direction. We show that at the $(010)$ and $(001)$ surfaces, an increase in the strain magnitude triggers a topological phase transition where the winding number of the surface-state spin texture is flipped while the four topological invariants characterizing the bulk band structure of the material are unchanged.