Effective continuous model on topological insulators

Abstract

Topological insulators are electronic materials that have a conventional energy gap as an insulator or semiconductor in the bulk, but possess gapless conducting states around their boundary. They are novel topological states of quantum matters and exhibit a series of exotic physics, such as quantum spin Hall effect, single valley Dirac fermions, Majorana fermions, topological magnetoelectric effect, etc. The conducting edge and surface states have topological origin of the electron band structure, and are protected by time-reversal symmetry such that they are robust or immune against local perturbation. In this dissertation, an effective continuous model for surface states is established from the three-dimensional modified Dirac model, and a theory of ultrathin film for topological insulators is developed. The established electronic model helps us explore spin physics of massive Dirac fermions. The theory has been successfully applied to explain an energy gap opening of the surface states in Bi2Se3 thin film in the measurement of angle-resolved photoemission spectroscopy (ARPES). In-gap bound states are also considered due to vacancy and impurity in topological insulators. It is found that a vacancy can always induce in-gap bound states in both two- and threedimensional topological insulators, and a half quantum magnetic flux inside the vacancy can result in helical Dirac zero modes. Finally the effect of random impurities on the surface transport in topological insulators is investigated, particularly the weak anti-localization of surface electrons in the quantum diffusion regime. It is found that the spin-orbit scattering may suppress the weak localization behaviors of massive Dirac fermions, which suggests an experiment to detect the weak localization in the topological insulator thin film.