Model for a First-Order Phase Transition to a Metallic Condensed State

A model for a first-order phase transition in an electron-hole gas is presented. It serves as a mean-field-theory description of the condensation of electron-hole droplets observed in highly excited germanium and silicon at liquid-helium temperatures. In this quantum model the Hartree-Fock exchange term provides the long-range attraction and the Pauli exclusion principle the short-range repulsion. Comparison is made with other mean-field theories, with other theoretical calculations on the electron-hole drop, and with the experimental data.