Double band inversion in the topological phase transition of Ge_1-x Sn_x alloys

¹ Department of Applied Physics, Nanjing University of Science and Technology - Nanjing 210094, China
² College of Electronic, Communication and Physics, Shandong University of Science and Technology Qingdao 266590, China
³ Department of Physics, University of Illinois at Urbana- Champaign - 1110 West Green Street, Urbana, IL 61801-3080, USA
⁴ Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana- Champaign 104 South Goodwin Avenue, Urbana, IL 61801-2902, USA

^(a) tcchiang@illinois.edu
^(b) phywangxx@njust.edu.cn

Received: 30 November 2020
Accepted: 30 January 2021

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.