Dirac Semimetal Phase in Rhombohedral $\beta -$Cu$_{2}$Se

Having been extensively studied during last decades in the fields of thermoelectics and ionic conductors, the $\alpha$ phase of Cu$_{2}$Se with antfluoride crystal structure has recently emerged as a topological zero-gap semimetal with a quadratic contact point which exists at the Fermi surface of its bulk electronic spectrum. Here we argue based on density functional electronic structure calculation that the $\beta$ phase of Cu$_{2}$Se realized in a recently discovered rhombohedral structure shows a Dirac semimetal behavior of the electrons near the Fermi level. These topological semimetals are currently generating a lot of interest due to unusual transport phenomena, such as strong quantum oscillations, large magnetoresistance effect and ultrahigh carrier mobilities with their Fermi velocities potentially exceeding graphene. We show that there exist Fermi arc states at the surface spectrum of $\beta -$Cu$_{2}$Se that are topologically protected by the bulk Dirac points. Their shape and spin properties should be resilient to the back- and side scattering effects in the surface transport, suggesting new ways for realizing high-mobility electronic devices.