Reorganization of the topological surface mode of topological insulating α-Sn

α-Sn is a topologically nontrivial semimetal in its natural structure. Upon compressively strained in plane, it transforms into a topological insulator. But, up to now, a clear and systematic understanding of the topological surface mode of topological insulating α-Sn is still lacking. In the present work, first-principle simulations are employed to investigate the electronic structure evolution of Ge1-xSnx alloys aiming at understanding the band reordering, topological phase transition and topological surface mode of α-Sn in detail. Progressing from Ge to Sn with increasing Sn content in Ge1-xSnx, the conduction band inverts with the first valence band and then with the second valence band sequentially, rather than inverting with the latter directly. Correspondingly, a topologically nontrivial surface mode arises in the first inverted band gap. Meanwhile, a fragile Dirac cone appears in the second inverted band gap as a result of the reorganization of the topological surface mode caused by the first valence band. The reorganization of the topological surface mode in α-Sn is very similar to the HgTe case. The findings of the present work are helpful for understanding and utilizing of the topological surface mode of α-Sn.