Nonequilibrium Green’s-function field equations for the coupled electron-hole-phonon system: A generalization of the shielded-potential approximation

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Abstract
We examine the microscopic quantum dynamics of a coupled electron-hole-phonon system using a nonequilibrium Green’s-correlation-function formulation, which incorporates the roles of electron-electron and hole-hole interactions along with electron-hole, electron-phonon, and hole-phonon interactions. Single-electron and single-hole Green’s-function field equations are derived, and we carry out a formal determination of the Green’s functions describing joint electron-hole propagation, two-electron propagation, and two-hole propagation, as well as treating the mixed Green’s-correlation function for one electron or one hole and a phonon state variable. A generalization of the shielded-potential approximation for the electron-hole-phonon system is discussed. In the absence of electron and hole vertex corrections, we obtain a closed system of equations for the self-consistent determination of the nonequilibrium single-electron and single-hole Green’s functions. This is in the nature of a self-consistent Born approximation accounting for electron-hole, electron-phonon, and hole-phonon scattering processes, dynamically screened by electron-electron and hole-hole interactions taking account of exchange phenomena. This formulation includes phenomenology such as phonon-mediated electron-hole, electron-electron, and hole-hole interactions, and it also includes provision for an external electric field E for future transport analysis.