Quantum spin Hall effect in two-dimensional hydrogenated SnPb alloy films

Abstract

Using first-principles calculations, we studied the geometric and band structures of 20 possible configurations of buckled hydrogenated SnPb alloy (Sn_xPb_8−xH₈) films. The configurations are topological insulators (TIs) when x ≥ 1. When x increases from 1 to 7, the band gap increases from 0.087 eV to 0.98 eV. The topological characteristics are suggested by s–p_xy band inversion and confirmed by helical edge states, which are time-reversal symmetry protected. According to spin–orbit coupling (SOC) analysis results, we draw the conclusion that the Pb atoms have greater SOC strength than the Sn atoms, so when the number ratio of Pb and Sn atoms is greater than 1/12 the SOC strength is large enough to trigger the band inversion between the s and p_xy orbitals, causing the SnPb alloy film to turn into a topological insulator (TI) from a normal band insulator (NI). We give a simple rule for the topological criterion of hydrogenated SnPb alloy films by comparing the ratio of Pb and Sn atoms. This would provide a useful reference for the design of topological devices based on NI–TI hetero-junctions for experiments.