Intermediate Polaronic Charge Transport in Organic Crystals from a Cumulant plus Green-Kubo First-Principles Approach
Predicting the electrical properties of organic molecular crystals (OMCs) is challenging due to their complex crystal structures and electron-phonon (e-ph) interactions. Charge transport in OMCs is conventionally categorized into two limiting regimes $-$ band transport, characterized by weak e-ph interactions and governed by low-energy intermolecular vibrations, and charge hopping, where strong e-ph interactions form localized polarons that diffuse slowly via thermally activated processes. However, between these two limiting cases there is a common, but less well understood intermediate transport regime where polarons are present but transport does not occur via hopping. Here we show accurate calculations of the carrier mobility in the intermediate transport regime, which contribute to shed light on its microscopic origin. We combine a finite-temperature cumulant method to describe the strong e-ph interactions and Green-Kubo transport calculations. Our study on naphthalene crystal demonstrates that we can accurately predict the electron mobility in the intermediate regime, within a factor of 1.5$-$2 of experiment between 100$-$300 K. Our analysis reveals that electrons couple strongly with both inter- and intramolecular phonons in the intermediate regime, as evidenced by the formation of a broad polaron satellite peak in the electron spectral function and by significant changes in the quasiparticle peak linewidth and spectral weight. These higher-order e-ph interactions make transport calculations based on the Boltzmann equation inadequate to describe the intermediate regime. Our study advances the understanding of the intermediate regime and paves the way for quantitative modeling of charge transport in complex organic crystals.