Bulk physics entwined with a topological surface state

TL;DR

This paper derives a microscopic relation between bulk and surface states in IV-VI semiconductors, revealing how bulk interactions and surface band bending can tune the spin textures of topological surface states.

Contribution

It provides an exact microscopic relation linking bulk wave functions to surface states and predicts tunable spin textures in SnTe's Dirac cones based on surface conditions.

Findings

Derived an exact relation between bulk and surface wave functions.

Predicted tunable spin textures in SnTe surface states.

Showed influence of bulk spin-orbit and surface band bending on spin-momentum locking.

Abstract

For the IV-VI semiconductor family we derive an exact relation between the microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl topological surface state wave function, thus obtaining a fully microscopic surface state. We find that the balance of spin-orbit interaction and crystal field in the bulk, and the band bending at the surface, can profoundly influence the surface state spin-momentum locking. As a manifestation of this we predict that the spin texture of the $M$-point Dirac cones of SnTe can be tuned through an unexpectedly rich sequence of spin textures -- warped helical with winding number $\pm 1$, $k_x$ linear, hyperbolic, and $k_y$ linear -- e.g. by tuning the band bending at the surface.