  The opening of a band gap due to compressive uniaxial strain renders bulk
HgTe a strong three-dimensional topological insulators with protected gapless
surface states at any surface. By employing a six-band k.p model, we determine
the spin textures of the topological surface states of strained HgTe using
their close relations with the mirror Chern numbers of the system and the
orbital composition of the surface states. We show that at surfaces with C2v
point group symmetry 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.
