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.Comment: 5 pages, 6 figure
