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).

Final, 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

References in corpus (21)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
• High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Electronic transport and quantum localization effects in organic semiconductors
• On the Munn-Silbey approach to polaron transport with off-diagonal coupling
• Crossover from Super- to Sub-Diffusive Motion and Memory Effects in Crystalline Organic Semiconductors
• Quantum mechanics of open systems: Dissipaton theories
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• A simple improved low temperature correction for the hierarchical equations of motion
• Transient localization from the interaction with quantum bosons
• Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations
• Cumulant expansion in the Holstein model: Spectral functions and mobility
• Jumping kinetic Monte Carlo: Fast and accurate simulations of partially delocalised charge transport in organic semiconductors
• Anomalous transport of small polarons arises from transient lattice relaxation or immovable boundaries
• Vertex corrections to conductivity in the Holstein model: A numerical-analytical study
• Precursors to Anderson Localization in the Holstein Model: Quantum and Quantum-Classical Solutions
• Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model

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