Coulomb interactions and generalized pairing in condensed matter

Proceeding from a coherent-state functional-integral approach we give a first-principles theory of generalized pairing phases in a dense neutral system of electrons and protons. Apart from a standard stationary phase approximation the approach is general, it requires no adiabatic separation of time scales, and it can be applied for arbitrary temperatures. For the resulting mean-field theory, we show that pairing of both electrons and protons is possible at low temperatures, and especially so when an appropriately defined electron-proton order parameter becomes sufficiently large. As a preliminary to the experimentally important case where the protons order in a crystalline phase, the case of continuous symmetry is first presented. Among generic results is the prediction, through a stability analysis, of a charge-density wave (and repairing), and the location of a critical point, both discussed in light of recent experiments on the high-pressure states of hydrogen.