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

TL;DR

This paper theoretically investigates how surface morphology affects topological electronic states on (Pb,Sn)Se (001) surfaces, explaining experimental phenomena like 1D states at step edges and the collapse of Dirac cones.

Contribution

It provides a theoretical model linking surface structure variations to topological state behavior and topological indices, explaining experimental observations.

Findings

Valley mixing depends on surface structure.

Emergence of 1D states at odd-height step edges.

Different topological indices characterize terraces.

Abstract

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.