Many-body Green's function analysis of the doped Fröhlich solid

In polar semiconductors and insulators, the Fröhlich interaction between electrons and long- wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearance of characteristic 'polaron satellites' in the spectral function. The simplest and most widely used model that captures these effects is the Fröhlich model, which focuses on undoped systems and ignores carrier screening and Pauli blocking effects that are present in real experiments on doped samples. To overcome this limitation, we have extended the Fröhlich model to the case of doped solids, allowing us to provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. In our analysis we compare two approaches, namely Dyson's equation with the Fan-Migdal self-energy, and the second order cumulant expansion.