A unified theory for charge-carrier transport in organic crystals

Abstract

To characterize the crossover from bandlike transport to hopping transport in molecular crystals, we study a microscopic model that treats electron-phonon interactions explicitly. A finite-temperature variational method combining Merrifield's transformation with Bogoliubov's theorem is developed to obtain the optimal basis for an interacting electron-phonon system, which is then used to calculate the bandlike and hopping mobilities for charge carriers. Our calculations on the one dimensional (1D) Holstein model at T=0 K and finite temperatures show that the variational basis gives results that compared favorably to other analytical methods. We also study the structures of polaron states at a broad range of parameters including different temperatures. Furthermore, we calculate the bandlike and hopping mobilities of the 1D Holstein model in different parameters and show that our theory predicts universal power-law decay at low temperatures and an almost temperature independent behavior at higher temperatures, in agreement with experimental observations. In addition, we show that as the temperature increases, hopping transport can become dominant even before the polaron state changes its character. Thus, our result indicates that the self-trapping transition studied in conventional polaron theories does not necessarily correspond to the bandlike to hopping transition in the transport properties in organic molecular crystals. Finally, a comparison of our 1D results with experiments on ultrapure naphthalene crystals suggests that the theory can describe the charge-carrier mobilities quantitatively across the whole experimental temperature range.