Non-magnetic impurities and in-gap bound states in topological insulators

In-gap bound states induced by non-magnetic impurities in various dimensional topological insulators are investigated based on a modified Dirac model that considers quadratic corrections to the mass term. Their existence and features greatly rely on the potential form of the impurity as well as the dimensionality of the topological insulator. It is analytically proven that the impurity potential modeled by the delta function can induce the bound states in one dimension (1D), but not in two and three. For a single non-magnetic impurity with a general isotropic potential, formal solutions are obtained and further numerical calculations are performed. In particular, the in-gap bound states induced by a non-magnetic impurity with isotropic Gaussian potentials in two-dimensional (2D) and three-dimensional (3D) topological insulators are numerically investigated. Information on how many in-gap bound states can be trapped by a non-magnetic Gaussian impurity is presented for the parameters from a series of topologically non-trivial materials.