Subsurface impurities and vacancies in a three-dimensional topological insulator

TL;DR

This study uses a microscopic lattice model to analyze how impurities and vacancies at various depths affect the electronic states in a three-dimensional topological insulator, revealing impurity-induced resonance states and modifications to the Dirac point.

Contribution

It provides a detailed analysis of impurity and vacancy effects at different depths in a 3D topological insulator, including the emergence of resonance states and Dirac point splitting, which was not previously characterized in such detail.

Findings

Impurity-induced resonance states appear at energies inversely proportional to impurity strength.

Deep impurities can split the Dirac point into two off-center nodes.

Vacancy clusters can host zero-energy resonance states, especially if fully symmetric.

Abstract

Using a three-dimensional microscopic lattice model of a strong topological insulator (TI) we study potential impurities and vacancies in surface and subsurface positions. For all impurity locations we find impurity-induced resonance states with energy proportional to the inverse of the impurity strength, although the impurity strength needed for a low-energy resonance state increases with the depth of the impurity. For strong impurities and vacancies as deep as 15 layers into the material, resonance peaks will appear at and around the Dirac point in the surface energy spectrum, splitting the original Dirac point into two nodes located off-center. Furthermore, we study vacancy clusters buried deep inside the bulk and find zero-energy resonance states for both single and multiple-site vacancies. Only fully symmetric multiple-site vacancy clusters show resonance states expelled from the bulk gap.