| Summary: | We present results of a microscopic tight-binding modeling of Bi $_{2}$ Se $_{3}$ three-dimensional topological insulator using a sp $^{3}$ Slater–Koster Hamiltonian, with parameters calculated from density functional theory. Based on the calculated atomic- and orbital-projections of the wavefunctions associated with valence- and conduction-band states at the center of the Brillouin zone, we propose a real-space description of band inversion for both bulk and a slab of finite thickness. A systematic analysis of the key features of the surface states, in particular the spatial distribution and the spin-character of the surface states wavefunction, is carried out for slabs of different thickness, ranging from one to tens of quintuple layers. We obtain an estimate of the slab thickness at which the energy gap induced by interaction between the top and bottom surface states becomes negligible, based on the present available numerical precision. We anticipate that this finding will be relevant for all microscopic calculations addressing the effect of external perturbations on the surface states near the Dirac point. The modifications in the helical spin-texture of the Dirac-cone surface states, in the form of in-plane and out-of-plane spin projections, are calculated as a function of the slab thickness. These calculations are important for the interpretation of ongoing experiments, which probe the spin-polarization of the surface states in topological insulator thin films.
|
|---|