Topological states on uneven (Pb,Sn)Se (001) surfaces

The impact of surface morphology on electronic structure of topological crystalline insulators is studied theoretically. As an example, the structure of topologically protected electronic states on a (001) (Pb,Sn)Se surface with terraces of atomic height is modeled. Within the envelope function model it is shown that valley mixing, the phenomenon responsible for the peculiar "double Dirac cone" shape of the surface state dispersion, depends crucially on the structure of the surface. By varying the width and the number of atomic layers in the terraces, a comprehensive explanation of recent experimental findings, i.e., the emergence of 1D states bound to odd-height atomic step edges as well as the collapse of "double Dirac cone" structure on a rough surface, is achieved. This approach allows us also to determine topological indices characterizing terraces and their interfaces. In the (001) surface of (Pb,Sn)Se the adjacent terraces turn out to be described by different values of the winding number topological invariant.