Importance of van der Waals interactions forab initiostudies of topological insulators

We investigate the lattice and electronic structures of the bulk and surface of the prototypical layered topological insulators Bi₂Se₃and Bi₂Te₃usingab initiodensity functional methods, and systematically compare the results of different methods of including van der Waals (vdW) interactions. We show that the methods utilizing semi-empirical energy corrections yield accurate descriptions of these materials, with the most precise results obtained by properly accounting for the long-range tail of the vdW interactions. The bulk lattice constants, distances between quintuple layers and the Dirac velocity of the topological surface states (TSS) are all in excellent agreement with experiment. In Bi₂Te₃, hexagonal warping of the energy dispersion leads to complex spin textures of the TSS at moderate energies, while in Bi₂Se₃these states remain almost perfectly helical away from the Dirac point, showing appreciable signs of hexagonal warping at much higher energies, above the minimum of the bulk conduction band. Our results establish a framework for unified and systematic self-consistent first principles calculations of topological insulators in bulk, slab and interface geometries, and provides the necessary first step towardab initiomodeling of topological heterostructures.