Metallic State of the Electron-Hole Liquid, Particularly in Germanium

We have calculated the ground-state energy of an electron-hole liquid. The kinetic and exchange energies are included exactly, and the correlation energy is estimated using Hubbard's modification of the random-phase approximation. In an isotropic electron-hole liquid, the metallic state is not bound relative to free excitons. In Ge the anisotropic band structure leads to a substantial binding of the metallic state. Application of a large $〈111〉$ strain to Ge reduces the situation to one resembling the isotropic case.