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Phonon spectral functions of photo-generated hot carrier plasmas: effects of carrier screening and plasmon-phonon coupling

We investigate spectral behavior of phonon spectral functions in an interacting multi-component hot carrier plasma. Dielectric polarization functions are formulated so that they satisfy Dyson equations of the effective interactions among plasma components. We find a useful sum rule giving simple relation between plasma-species resolved dielectric functions. Spectral analysis of various phonon spectral functions is performed considering carrier-phonon channels of polar and nonpolar optical phonons, acoustic deformation-potential, and piezoelectric Coulomb couplings. Effects of phonon self-energy corrections are examined at finite temperature within a random phase approximation extended to include the effects of dynamic screening, plasmon--phonon coupling, and local-field corrections of the plasma species. We provide numerical data for the case of a photo-generated electron-hole plasma formed in a wurtzite GaN. Our result shows clear significance of the multiplicity of the plasma species in the dielectric response and phonon spectral functions of a multi-component plasma.