Double band inversion in the topological phase transition of Ge1-x Snx alloys

Abstract

We use first-principles simulation and alchemical mixing approximation to reveal the unique double band inversion and topological phase transition in GeSn alloys. Wave function parity, spatial charge distribution and surface state spectrum analyses suggest that the band inversion in GeSn is relayed by its first valence band. As the system evolves from Ge to -Sn, its conduction band moves down, and inverts with the first and the second valence bands consecutively. The first band inversion makes the system nontrivial, while the second one does not change the topological invariant of the system. Both of the band inversions yield surface modes spanning the individual inverted gaps, but only the surface mode in the upper gap associates with the nontrivial nature of tensile-strained -Sn.