Quantum spin Hall effect in strained (111)-oriented SnSe layers

Abstract

Recently, the quantum spin Hall effect has been predicted in (111)-oriented thin films of SnSe and SnTe topological crystalline insulators. It was shown that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness -- the calculated topological invariant indexes and edge state spin polarizations show that for films 20-40 monolayers thick a two-dimensional topological insulator phase appears. Edge states with Dirac cones with opposite spin polarization in their two branches are obtained for both materials. However, for all but the (111)-oriented SnTe films with an even number of monolayers an overlapping of bands in $\overline{\Gamma}$ and $\overline{\mathrm{M}}$ diminishes the final band gap and the edge states appear either against the background of the bands or within a very small energy gap. Here we show that this problem in SnSe films can be removed by applying an appropriate strain. This should enable observation of the Quantum Spin Hall effect also in SnSe layers.