Charge carrier mobility in systems with local electron-phonon interaction

We present a method for calculation of charge carrier mobility in systems with local electron-phonon interaction. The method is based on unitary transformation of the Hamiltonian to the form where the nondiagonal part can be treated perturbatively. The Green's functions of the transformed Hamiltonian were then evaluated using the Matsubara Green's functions technique. The mobility at low carrier concentration was subsequently evaluated from Kubo's linear response formula. The methodology was applied to investigate the carrier mobility within the one-dimensional Holstein model for a wide range of electron-phonon coupling strengths and temperatures. The results indicated that for low electron-phonon coupling strengths the mobility decreases with increasing temperature, while for large electron-phonon coupling the temperature dependence can exhibit one or two extremal points, depending on the phonon energy. Analytical formulas that describe such behavior were derived. Within a single framework, our approach correctly reproduces the results for mobility in known limiting cases, such as band transport at low temperatures and weak electron-phonon coupling and hopping at high temperatures and strong electron-phonon coupling.