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 recently discovered topological crystalline insulator. Apart from the (001) surface states previously studied, two other surface families, 011 and 111, in which the mirror symmetry of the crystal's rocksalt 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.