Topologicalα-Sn surface states versus film thickness and strain

Abstract

The theoretical prediction that gray tin represents a strong topological insulator under strain [L. Fu and C.L. Kane, Phys. Rev. B 76, 045302 (2007)] is proven for biaxially strained $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ layers with varying thickness by means of a generalized density functional theory with a nonlocal exchange-correlation potential that widely simulates quasiparticle bands and a tight-binding method including intra- and interatomic spin-orbit interaction. Hydrogen-passivated surfaces are modeled by symmetric slabs. In contrast to the conventional picture of a topological insulator, we find topological gapless surface states below the strain-induced bulk gap, in agreement with photoemission studies. The topological surfaces states do not emerge out of the lower ${\ensuremath{\Gamma}}_{8}^{+}$ states but are strongly influenced by the inverted bulk ${\ensuremath{\Gamma}}_{7}^{\ensuremath{-}}$ band, i.e., lie within the negative bulk $sp$ gap. We show that the position of the Dirac point and the dispersion of the surrounding bands depend on the thickness of the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ layer but are less influenced by strain. The resulting Fermi velocities agree well with available photoemission data.