Abstract
Topological insulators are electronic materials that have conventional energy gap as insulators 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.
In this talk, we establish an effective continuous model for surface states from the three-dimensional modified Dirac model, and develop a theory of ultrathin film for topological insulators. The theory has been used successfully to explain the energy gap opening of the surface states in Bismuth Selenide thin film in the measurement of angle-resolved photoemission spectroscopy (ARPES). We also consider the vacancy effect in topological insulators. It is found that a vacancy can always induce in-gap bound states in both two- and three-dimensional topological insulators, and a half-quantum magnetic flux inside the vacancy can result in helical Dirac zero modes. Finally we investigate the effect of random impurities on the surface transport in topological insulators, particularly the weak antilocalization 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.