Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach

Abstract

Studying charge transport in models with nonlocal carrier--phonon interaction is difficult because it requires finite-temperature real-time correlation functions of mixed carrier--phonon operators. Focusing on models with discrete undamped phonon modes, we show that such correlation functions can be retrieved from the hierarchical equations of motion (HEOM), although phonons have been integrated out. Our procedure relies on the general explicit expression of HEOM auxiliaries in terms of phonon creation and annihilation operators. It reveals that the auxiliaries describe multiphonon-assisted carrier transitions induced by genuine many-phonon correlations, from which lower-order correlations are subtracted according to the finite-temperature Wick's theorem. Applying the procedure to our recently developed momentum-space HEOM method featuring appropriate hierarchy closing, we compute the numerically exact dynamical mobility of a carrier within the one-dimensional Peierls model. The carrier mobility at moderate temperatures decreases with increasing interaction, whereas high temperatures see the opposite trend, reflecting the prevalence of the phonon-assisted current over the purely electronic band current. The pronounced finite-size effects and HEOM instabilities delimit the range of applicability of our approach to moderate interactions, moderate to high temperatures, and not too fast phonons. Importantly, this range comprises the values relevant for charge transport in crystalline organic semiconductors, and we present and discuss the corresponding numerically exact results in a companion paper (arXiv:2501.05055).

arXiv commentFinal, published version; Main text: 28 pages, 8 figures; Supplemental material: 7 pages, 2 figures; This submission is accompanied by Part II. Numerically exact quantum dynamics in the slow-phonon regime (arXiv:2501.05055); The data that support the findings of this study are openly available at https://doi.org/10.5281/zenodo.14637019

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Cited by in corpus (5)

• Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime
• Identification of the transport regimes of the one-dimensional Holstein model
• Numerically "exact" charge transport dynamics in a dissipative electron-phonon model rationalizing the success of the transient localization scenario
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems