Effect of electronic concentration on the self-trapping transition of polaron for the weakly correlated system in the adiabatic limit

Abstract

The self-trapping transition of the polaron is investigated for the two-dimensional extended Holstein-Hubbard model. A series of canonical transformations are performed on the Hamiltonian followed by a many phonon averaging, to eliminate the phonon degrees of freedom from the system. The mean field Hartree-Fock calculation has been done to solve the effective electronic Hamiltonian and the ground state energy is obtained variationally. The effect of electronic concentration on the polaronic hopping parameter is studied with respect to the electron–phonon interaction strengths in the weak Coulomb correlation limit. The transition from a delocalized mobile polaron to a localized self-trapped polaron has been found to be discontinuous for the adiabatic motion of the polaron and the self-trapping transition needs stronger electron–phonon interaction strength as the electronic concentration minimizes.