Density dependence of the optical absorption of an interacting many-polaron gas

The optical absorption of a many (continuum) polaron gas is derived in the framework of a variational approach at zero temperature and weak electron-phonon coupling strength. We derive a compact formula for the optical conductivity of the many-polaron system, taking into account many-body effects in the electron or hole system. Within the method presented here, these effects are contained completely in the dynamical structure factor of the electron or hole system. This allows one to build on well-established studies of the interacting electron gas. Based on this approach a feature in the absorption spectrum of the many-polaron gas, related to the emission of a plasmon together with a phonon, is identified. As an application and illustration of the technique, we compare the theoretical many-polaron optical absorption spectrum as derived in the present work with the $``d$-band'' absorption feature in ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}} (\ensuremath{\delta}l0.004).$ Similarities are shown between the theoretically and the experimentally derived first frequency moment of the optical absorption of a family of differently doped ${\mathrm{Nd}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ materials.