Many-body corrected tight-binding Hamiltonians for an accurate quasiparticle description of topological insulators of the Bi2Se3 family

Abstract

We generate many-body corrected tight-binding Hamiltonians for topological insulators of the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ family. To this end, we use ab initio calculated parameters extracted from $GW$ calculations, thus capturing many-body exchange and correlation effects, in contrast to previous tight-binding models. We investigate the effect of many-body renormalizations on the electronic structure of bulk and surface states of semi-infinite systems as well as thin films of these materials. It is shown that the $GW$ self-energy correction brings about profound changes not only in the band-gap values but also in the band dispersion around the inverted gaps with respect to standard density-functional theory (DFT). These changes substantially improve the agreement with experiment. We discuss the strong renormalization effect as being a result of the characteristic overestimation of inverted gaps by standard approximations of DFT (opposite to the underestimation of gaps in topologically trivial materials). In particular, we analyze the consequences that these renormalizations have on the dispersions of the topological surface states and on the surface resonances. For reference, the tight-binding Hamiltonians are provided in the Supplemental Material [30].