Low-Energy Polaron Spectra in the Doped Fröhlich Model*

We investigate the low-energy electron quasiparticle spectrum of the doped
Fröhlich solid as a model system for electron-phonon coupling in doped polar
semiconductors. Substantial improvements in the resolution of photoemission
spectroscopy have given access to the low-energy physics in these
systems, and have shown that electron-phonon interactions are at the core of a
wide range of intriguing properties, from high electron mobility to superconductivity.
In view of these advances, a sound theoretical description of energy levels and
effective masses in the doped Fröhlich solid is called for. In our study, we present
analytical results for the momentum-resolved spectral function as obtained from the
interacting electron Green’s function. We employ both the first-order
Migdal approximation and the higher-order Cumulant Expansion approach.
We find that the treatment of polaron satellites using the Cumulant Expansion achieves
much better agreement with experiment, albeit at the price of a poorer description of
quasiparticle dispersion relations.