Maximally localized Wannier functions for describing a topological phase transition in stanene

Abstract

Starting from first-principles calculations on pristine stanene and using maximally localized Wannier functions (MLWFs), we analyze the different phases of the system when it is driven to a topological phase transition. The transition is achieved by a continuous parameter represented by an external electric field ${\mathcal{E}}_{z}$ as a generic inversion-symmetry-breaking term. We also compare the results with those of a multiorbital tight-binding (TB) model for stanene, whose hopping integrals are determined by Slater-Koster parameters. The system is in a topological (trivial) phase for ${\mathcal{E}}_{z}<{\mathcal{E}}_{c}$ (${\mathcal{E}}_{z}>{\mathcal{E}}_{c}$). We obtain that the critical field is ${\mathcal{E}}_{c}\ensuremath{\simeq}0.69\phantom{\rule{4pt}{0ex}}\mathrm{eV}/\AA{}$ for the more realistic MLWF compared to ${\mathcal{E}}_{c}\ensuremath{\simeq}0.15\phantom{\rule{4pt}{0ex}}\mathrm{eV}/\AA{}$ in the TB model. This suggests a larger stability of the topological phase of stanene when deposited on inert substrates.