Surface and interface states of Bi$_{2}$Se$_{3}$ thin films investigated by second harmonic generation

Topological insulators (TIs) behave as a charge-gapped insulator in its interior, but hosting a spin-momentum-locked Dirac state at the surface. When the Fermi level crosses over conduction/valence band, undesirable bulk charge transport disturbs to exploit the surface nature, so that thin film TIs have been highlighted as a method to reduce bulk carrier effect due to large surface to volume ratio. In this presentation, we discuss surface and/or interface states for Bi$_{2}$Se$_{3}$ in form of film by exploiting second harmonic generation technique. Based on nonlinear susceptibility deduced from the model fitting, we investigate the details of band bending such as its direction and strength which were further addressed by examining terahertz field profile emitted from the sample. Finally, we discuss the evolution of these properties as a function of film thickness.