Electron-hole liquid as a true ground state

Electron-hole-liquid (EHL) theory is shown to predict a first-order semiconductor-to-semimetal phase transition at a critical value of the fundamental (indirect) energy gap with a finite minimum value of the band overlap in the semimetallic phase. The consistency of this result with density-functional theory is discussed. The theory is applied to ScN. The ground-state density of the EHL is computed to be lower than ${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$, which compares well with the smallest observed density of free carriers in this compound.