Many-body theory of energy relaxation in an excited-electron gas via optical-phonon emission

We consider relaxation of a hot-electron gas by emission of LO phonons in quasiequilibrium when both the electrons and the lattice are in separate internal equilibria, and the electron distribution function can be described by an effective temperature. We find that, in addition to dynamical screening and the hot-phonon effect, the many-body renormalization of the LO phonons also plays a crucial role, both qualitatively and quantitatively, in the power-loss process at low electron temperatures. The density of states of a LO phonon coupled to an electron gas has three branches: (i) the bare-phonon-like branch near the bare-phonon energy, (ii) the plasmonlike branch near the plasmon energy, and (iii) the low-energy quasiparticle-excitation-like branch in the quasiparticle-excitation region. We show that even though the oscillator strengths of the plasmonlike and the quasiparticle-excitation-like branches are extremely small, they dominate the power-loss process at low enough electron temperatures. This produces an enhancement of the power loss at low electron temperatures by many orders of magnitude relative to the power loss to bare unrenormalized LO phonons. We believe that the hot-electron relaxation experiments are a very suitable way of studying the novel quasiparticle-like LO phonons, which are unlikely to be observed directly because of their small oscillator strength. We provide a detailed quantitative theory for hot-electron relaxation in both two- and three-dimensional systems based on this many-body approach and find quantitative agreement with existing experimental results in the 20200-K electron-temperature regime.