Quantum Spin Hall Insulators in Tin Films: Beyond Stanene

Abstract

Large-gap quantum spin Hall (QSH) insulators were previously predicted in stanene and its derivatives. Beyond stanene that is the thinnest $\alpha$-Sn(111) film, we propose to explore QSH insulators in $\alpha$-Sn films with different crystallographic orientations. Our first-principles calculations reveal that the thickness-dependent band gap of $\alpha$-Sn (100) and (110) films does not show a monotonic decrease as typically expected by quantum confinement, but displays an oscillating change behavior, an indicative of topological quantum phase transition. While these films are normal insulators in the ultrathin limit, the QSH phase emerges above a critical film thickness of around 10 layers. Remarkably, the QSH insulators are obtainable within a wide thickness range and their energy gaps are sizable (even $>$0.1 eV), which facilitates experimental realization of the high-temperature QSH effect.