The effect of electric potential on Landau levels for topological insulator surface states

We study the effect of an electric potential well on the Landau level (LL) spectrum for surface states of a three-dimensional (3D) topological insulator (TI) by using a method of numerical diagonalization for the Hamiltonian in a truncated Hilbert space. It is found that the dispersivity of energy is dependent on the position of electron cyclotron orbit center (COC). A dispersionless energy spectrum like flat LLs appeared as if without the confining potential when the electron COC is far away from the well boundaries (corners). When the electron COC is near the boundaries, however, there exist some interesting interface states propagating along the well due to the presence of electric confinement which causes quantized subband mixing. Moreover, the probability density and the spin polarization of interface states in conduction band oscillate mainly inside the well and decay outside, while those in valence band oscillate outside and decay inside. These findings here may provide a further understanding of 3D TI surface states.