Optical conductivity and Raman spectra of coupled electron-phonon systems via bosonic algebra

The sea-boson technique is used to compute the optical conductivity and Raman spectra of an interacting electron gas coupled with longitudinal optical phonons. The Hamiltonian is transformed from the fermionic representation to a bosonic representation in which the new dispersion of particle-hole excitations appears. The equations of motion of currents and densities in terms of sea bosons are constructed and the optical conductivity and Raman spectra are deduced. The sea-boson method is more convenient to deal with since the interacting Hamiltonian is purely quadratic in these bosons. For Raman scattering, we obtain the same random-phase approximation results as reported previously using the fermionic method, but with less cumbersome algebra. For the optical conductivity, our results automatically capture the Fano-resonance effect caused by the interference between the continuum excitations involving a particle-hole pair plus a phonon and the nearly discrete two-phonon excitations.