Charge Transport in Interacting Electron–Phonon Models. Insights Offered by Hierarchical Equations of Motion

Phonon-limited charge mobility is determined by the finite-temperature real-time current autocorrelation function, whose computations often rely on approximations of unknown domain of validity.

We describe how the hierarchical equations of motion (HEOM) method yields numerically exact charge mobility in one-dimensional electron–phonon models with discrete undamped phonon modes [1]. Our results are representative of the long-chain limit and fully capture the crossover from ballistic to diffusive charge dynamics. This is made possible by formulating the HEOM in momentum space and stabilizing them by an appropriate closing scheme.

Considering the diagonal dynamic disorder (the Holstein model) at moderate adiabaticity ratios, we find that vertex corrections do not significantly change the mobility predicted by the dynamical mean-field theory, yet significantly affect the details of the ballistic-to-diffusive crossover [2]. Considering the off-diagonal dynamic disorder (the Peierls model), which influences charge transport in organic semiconductors, we devise a proper treatment of the phonon-assisted current, and analyze the relative importance of band and phonon-assisted contributions to mobility.