On the basis of the two-site polaron problem, which we solve by exact diagonalization, we analyze the spectral properties of polaronic systems in view of discerning localized from itinerant polarons and bound polaron pairs from an ensemble of single polarons. The corresponding experimental techniques for that concern photoemission and inverse photoemission spectroscopy. The evolution of the density of states as a function of concentration of charge carriers and strength of the electron-phonon interaction clearly shows the opening up of a gap between single-polaronic and bipolaronic states, in analogy to the Hubbard problem for strongly correlated electron systems. In studying the details of the intricately linked dynamics of the charge carriers and of the molecular deformations which surround them, we find that in general the dynamical delocalization of the charge carriers helps to strengthen the phase coherence for itinerant polaronic states, except for the crossover regime between adiabatic and antiadiabatic small polarons. The crossover between these two regimes is triggered by two characteristic time scales: the renormalized electron hopping rate and the renormalized vibrational frequency becoming equal. This crossover regime is then characterized by temporarily alternating self-localization and delocalization of the charge carriers which is accompanied by phase slips in the charge and molecular deformation oscillations and ultimately leads to a dephasing between these two dynamical components of the polaron problem. We visualize these features by a study of the temporal evolution of the charge redistribution and the change in molecular deformations. The spectral and dynamical properties of polarons discussed here are beyond the applicability of the standard Lang-Firsov approach to the polaron problem.

DOI:https://doi.org/10.1103/PhysRevB.55.14872