Topological Dirac semimetal phase in Ge<italic>x</italic>Sn<italic>y</italic> alloys.

Recently, two stable allotropes (germancite and stancite) for the group IV elements (Ge and Sn) with a staggered layered dumbell structure were proposed to be three-dimensional (3D) topological Dirac semimetals [Phys. Rev. B <bold>93</bold>, 241117 (2016)]. A pair of Dirac points is on the rotation axis away from the time-reversal invariant momentum, and the stability of the 3D bulk Dirac points is protected by the <italic>C</italic>3 rotation symmetry. Here, we use the first principles calculations to investigate Ge<italic>x</italic>Sn<italic>y</italic> alloys which share the same rhombohedral crystal structure with the space group of D 3 d 6 . Six Ge<italic>x</italic>Sn<italic>y</italic> alloys are predicted to be energetically and dynamically stable, where (<italic>x</italic>, <italic>y</italic>) = (8, 6) and (6, 8) and the <italic>α</italic> and <italic>β</italic> phases of (10, 4) and (4, 10). Our results demonstrate that all the six Ge<italic>x</italic>Sn<italic>y</italic> alloys are topological Dirac semimetals. The different nontrivial surface states and surface Fermi arcs are identified. Our work will substantially enrich the family of 3D Dirac semimetals which are within the reach of experimental realization. [ABSTRACT FROM AUTHOR]