Polaron crossover in molecular solids

Abstract

An analytical variational method is applied to the molecular Holstein Hamiltonianin which the dispersive features of the dimension dependent phonon spectrumare taken into account by a force constant approach. The crossover between alarge and a small size polaron is monitored, in one, two and three dimensionsand for different values of the adiabatic parameter, through the behaviour of theeffective mass as a function of the electron–phonon coupling. By increasing thestrength of the intermolecular forces the crossover becomes smoother and occurs athigher e–ph couplings. These effects are more evident in three dimensions. Weshow that our modified Lang–Firsov method starts to capture the occurrence of apolaron self-trapping transition when the electron energies become of order of thephonon energies. The self-trapping event persists in the fully adiabatic regime. Atthe crossover we estimate polaron effective masses of order times the bare band mass according to the dimensionality and the value of the adiabaticparameter. Modified Lang–Firsov polaron masses are substantially reduced intwo and three dimensions. There is no self-trapping in the antiadiabatic regime.