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

TL;DR

This paper reveals a unique double band inversion process in Ge1-xSnx alloys during topological phase transition, showing how the system's electronic structure evolves and affects surface states.

Contribution

It introduces the first detailed analysis of double band inversion in Ge1-xSnx alloys and its implications for topological properties using first-principles simulations.

Findings

Double band inversion occurs during the transition from Ge to α-Sn.

The first valence band drives the initial band inversion and topological change.

Only the surface mode in the upper gap relates to the nontrivial topological phase.

Abstract

We use first-principles simulation and virtual crystal approximation to reveal the unique double band inversion and topological phase transition in Ge1-xSnx alloys. Wavefunction parity, spatial charge distribution and surface state spectrum analyses suggest that the band inversion in Ge1-xSnx is relayed by its first valence band. As the system evolves from Ge to {\alpha}-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 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 {\alpha}-Sn.