Electronic structures of Ge1−xSnx alloys (0 ≤ x ≤ 1) are theoretically studied by nonlocal empirical pseudopotential method. For relaxed Ge1−xSnx, a topological semimetal is found for x > 41% with gapless and band inversion at Γ point, while there is an indirect-direct bandgap transition at x = 8.5%. For strained Ge1−xSnx on a Ge substrate, semimetals with a negative indirect bandgap appear for x > 43%, and the strained Ge1−xSnx on Ge is always an indirect bandgap semiconductor for x < 43%. With appropriate biaxial compressive strains, a topological Dirac semimetal is found with band inversion at Γ and one pair of Dirac cones along the [001] direction.
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