Many-body large polaron optical conductivity in SrTi$_{1-x}$Nb$_x$O$_3$

Recent experimental data on the optical conductivity of niobium doped SrTiO$_{3}$ are interpreted in terms of a gas of large polarons with effective coupling constant $\alpha_{eff}\approx2$. The {theoretical approach takes into account} many-body effects, the electron-phonon interaction with multiple LO-phonon branches, and the degeneracy and the anisotropy of the Ti t$_{2g}$ conduction band. {Based on the Fr\"{o}hlich interaction, the many-body large-polaron theory} provides an interpretation for the essential characteristics, except -- interestingly -- for the unexpectedly large intensity of a peak at $\sim130$ meV, of the observed optical conductivity spectra of SrTi$_{1-x}$Nb$_{x}$O$_{3}$ \textit{without} any adjustment of material parameters.