Electronic structure near an impurity and terrace on the surface of a three-dimensional topological insulator

Abstract

Motivated by recent scanning tunneling microscopy experiments on surfaces of ${\text{Bi}}_{1\ensuremath{-}x}{\text{Sb}}_{{x}^{\ensuremath{'}}}$ and ${\text{Bi}}_{2}{\text{Te}}_{3}$, we theoretically study the electronic structure of a three-dimensional (3D) topological insulator in the presence of a local impurity or a domain wall on its surface using a 3D lattice model. While the local density of states (LDOS) oscillates significantly in space at energies above the bulk gap, the oscillation due to the in-gap surface Dirac fermions is very weak. The extracted modulation wave number as a function of energy satisfies the Dirac dispersion for in-gap energies and follows the border of the bulk continuum above the bulk gap. We have also examined analytically the effects of the defects by using a pure Dirac fermion model for the surface states and found that the LDOS decays asymptotically faster at least by a factor of $1/r$ than that in normal metals, consistent with the results obtained from our lattice model.