Topological Insulators: Electronic Band Structure and Spectroscopy

In this study, we present the results of our ab initio calculation of the elastic constants, density of states, charge density, and Born effective charge tensors for ferroelectric (rhombohedral) and paraelectric phases (cubic) of the narrow band ferroelectrics (GeTe, SnTe) pseudopotentials. The related quantities such as bulk modulus and shear modulus using obtained elastic constants have also been estimated in the present work. The total and partial densities of states corresponding to the band structure of Sn(Ge)Te(S,Se) were calculated. We also calculated the Born effective charge tensor of an atom (for instance, Ge, Sn, Te, etc.), which is defined as the induced polarization of the solid along the main direction by a unit displacement in the perpendicular direction of the sublattice of an atom at the vanishing electric field. (paper)