The topological-crystalline-insulator (Pb,Sn)Te - surface states and their spin-polarization

Using a tight-binding approach we study theoretically the nature of surface states in Pb0.4Sn0.6Te - the newly discovered topological-crystalline-insulator. Apart from the studied before (001) surface states, two other surface families, {011} and {111}, in which the mirror symmetry of the crystal's rock-salt structure plays the same role in topological protection, are considered. Our calculations show that while in (111) surface states of (Pb,Sn)Te four single topologically protected Dirac-cones should appear, for the (110) surface states the protection is lifted for two L points. In this case, instead of the Dirac points energy gaps occur in the surface states, due to the interaction between the two L valleys. In all studied cases a chiral spin texture is obtained.