Anisotropy effects in phonon-assisted charge-carrier transport in organic molecular crystals

We present a theoretical description of polaron dc conductivities in organic molecular crystals. Our approach is based on a rigorous evaluation of the Kubo formula for electrical conductivity within a mixed Holstein-Peierls model. It generalizes the result of Holstein's local-coupling theory by treating both local and nonlocal electron-phonon interactions nonperturbatively. The general theory is supplemented by an application to a simplified model crystal in order to emphasize the essential physics. Accompanied by an illustrative numerical example, special emphasis is put on the emergence of anisotropy effects in the temperature dependence of the conductivity tensor. These anisotropy effects are shown to originate from phonon-assisted currents due to the nonlocal electron-lattice interaction which demonstrates the importance to go beyond local-coupling theories in order to describe the experimental observations.