Electrostatic effects and band bending in doped topological insulators

We investigate the electrostatic effects in doped topological insulators by developing a self-consistent scheme for an interacting tight-binding model. The presence of bulk carriers, in addition to surface electrons, generates an intrinsic inhomogeneous charge density in the vicinity of the surface and, as a result, band-bending effects are present. We find that electron doping and hole doping produce band-bending effects of similar magnitude and opposite signs. The presence of additional surface dopants breaks this approximate electron-hole symmetry and dramatically affects the magnitude of the band bending. Application of a gate potential can generate a depletion zone characterized by a vanishing carrier density. We find that the density profile in the transition zone between the depleted region and the bulk is independent of the applied potential. In thin films the electrostatic effects are strongly dependent on the carrier charge density. In addition, we find that substrate-induced potentials can generate a Rashba-type spin-orbit coupling in ultrathin topological insulator films. We calculate the profiles of bulk and surface states in topological insulator films and identify the conditions corresponding to both types of state being localized within the same region in space.