Finite size effects of the surface states in a lattice model of topological insulator

Energy gap and wave function in thin films of topological insulator is studied, based on tight-binding model. It is revealed that thickness dependence of the magnitude of energy gap is composed of damping and oscillation. The damped behavior originates from the presence of gapless surface Dirac cone in the infinite thickness limit. On the other hand, the oscillatory behavior stems from electronic properties in the thin thickness limit.