Franck-Condon factors as spectral probes of polaron structure

We apply the Merrifield variational method, to the Holstein molecular crystal model in D dimensions to compute nonadiabatic polaron band energies and Franck-Condon factors at general crystal momenta. We analyze these observable properties to extract characteristic features related to polaron self-trapping and potential experimental signatures. These results are combined with others obtained by the Global-Local variational method in 1D to construct a polaron phase diagram encompassing all degrees of adiabaticity and all electron-phonon coupling strengths. The polaron phase diagram so constructed includes disjoint regimes occupied by small polarons, large polarons, and a newly-defined class of compact polarons, all mutually separated by an intermediate regime occupied by transitional structures.