Quantum spin Hall effect in IV-VI topological crystalline insulators

Abstract

We envision that the quantum spin Hall effect should be observed in (111)-oriented thin films of SnSe and SnTe topological crystalline insulators. Using a tight-binding approach supported by firstprinciples calculations of the band structures, we demonstrate that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness. These results as well as 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. In this range of thicknesses in both SnSe and SnTe, (111)-oriented films edge states with Dirac cones with opposite spin polarization in their two branches are obtained. While in the SnTe layers a single Dirac cone appears at the projection of the Γ point of the two-dimensional Brillouin zone, in the SnSe (111)oriented layers three Dirac cones at M points projections are predicted.

Electronic properties of SnTe-class topological crystalline insulator materials

“…13(a), all the thin films with an even number of layers between 14 and 30 layers are QSH insulators. The similar results apply to the odd-layer thin film 90 , and even the SnSe (111) film 91 . The mechanism for realizing the QSH phase in TCI thin films through the intersurface coupling is similar to the thin films of Bi 2 Se 3 -class TIs [92][93][94] .…”

Correlation effects on topological crystalline insulators

“…Recent first-principles calculations predict that quantum spin Hall states can be realized in the (111) thin films of the SnTe class of three-dimensional topological crystalline insulators [41,42]. The surface Dirac fermions on the top and bottom surfaces of the (111) thin films are gapped by intersurface coupling and turn into a topological state.…”

“…Motivated by first-principles calculations [41,42] predicting that thin films of SnTe become two-dimensional topological insulators (i.e., quantum spin Hall insulators), they studied stability of gapless edge states with internal Z 2 symmetry that comes from reflection symmetry about the two-dimensional plane; they obtained Z 4 classification for thin films. Furthermore, they have developed a theoretical approach to classify three-dimensional topological crystalline insulators which utilizes the stability analysis of the gapless edge states.…”

Electrically tunable quantum spin Hall state in topological crystalline insulator thin films

“…Note added: After the completion of this work 45 , we learned of an independent work on (111) thin films of TCIs without the external electric field 46 .…”