Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping

TL;DR

This study examines how non-magnetic impurities affect the surface Dirac states of SnTe topological crystalline insulators, revealing energy shifts, confinement effects, and differences between slab and semi-infinite geometries through ab initio and continuum models.

Contribution

It provides a comprehensive analysis of impurity effects on surface states in SnTe, combining first-principles simulations with continuum models to reveal energy shifts and confinement phenomena.

Findings

Dirac cones shift down in energy upon doping

Impurity band width exhibits even-odd behavior based on impurity position

Surface states remain gapless in semi-infinite geometry, but gaps open in slabs due to hybridization

Abstract

We investigate the effect of a non-magnetic donor impurity located at the surface of the SnTe topological crystalline insulator. In particular, the changes on the surface states due to a Sb impurity atom are analyzed by means of ab initio simulations of pristine and impurity-doped SnTe. Both semi-infinite and slab geometries are considered within the first-principles approach. Furthermore, minimal and Green's function continuum models are proposed with the same goal. We find that the Dirac cones are shifted down in energy upon doping; this shift strongly depends on the position of the impurity with respect to the surface. In addition, we observe that the width of the impurity band presents an even-odd behavior by varying the position of the impurity. This behavior is related to the position of the nodes of the wave function with respect to the surface, and hence it is a manifestation of confinement effects. We compare slab and semi-infinite geometries within the ab initio approach, demonstrating that the surface states remain gapless and their spin textures are unaltered in the doped semi-infinite system. In the slab geometry, a gap opens due to hybridization of the states localized at opposite surfaces. Finally, by means of a continuum model, we extrapolate our results to arbitrary positions of the impurity, clearly showing a non-monotonic behavior of the Dirac cone.