First-principles studies of the three-dimensional strong topological insulators Bi₂Te₃, Bi₂Se₃and Sb ₂Te₃

Bi₂Te₃, Bi₂Se₃ and Sb ₂Te₃compounds have recently been predicted to be three-dimensional (3D) strong topological insulators. In this paper, based on ab initio calculations, we study in detail the topological nature and the surface states of this family of compounds. The penetration depth and the spin-resolved Fermi surfaces of the surface states are analyzed. We also present a procedure from which a highly accurate effective Hamiltonian can be constructed based on projected atomic Wannier functions (which keep the symmetries of the systems). Such a Hamiltonian can be used to study the semi-infinite systems or slab-type supercells efficiently. Finally, we discuss the 3D topological phase transition in the Sb₂(Te_1-xSe_x)₃ alloy system.