Confined states and spin polarization on a topological insulator thin film modulated by an electric potential

We study the electronic structure and spin polarization for surface states of a three-dimensional topological insulator (TI) thin film modulated by an electrical potential well. By routinely solving the low energy surface Dirac equation for the system, we demonstrated that there exist confined surface states in which the electron density is nearly localized inside the well and is exponentially decayed outside in real space, and their subband dispersions are quasilinear with respect to the propagating wavevector. Interestingly, the top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces. Along with the mathematical analysis, we provide an intuitive, topological understanding of the effect.