Charge transport limited by nonlocal electron-phonon interaction. II. Numerically exact quantum dynamics in the slow-phonon regime

TL;DR

This paper investigates charge transport in soft semiconductors influenced by slow phonons, revealing a transient superdiffusive to subdiffusive crossover and limitations of the transient localization scenario compared to exact quantum dynamics.

Contribution

The study applies a hierarchical equations of motion approach to accurately analyze quantum charge transport near the adiabatic limit, highlighting the transient nature of superdiffusive to subdiffusive crossover.

Findings

Transport exhibits a superdiffusive to subdiffusive crossover.

TLS approximates HEOM well at higher temperatures and stronger interactions.

Diffusive motion emerges from superdiffusive side within phonon timescales.

Abstract

Transport of charge carriers in mechanically soft semiconductors is mainly limited by their interaction with slow intermolecular phonons. Carrier motion exhibits a crossover from superdiffusive to subdiffusive, producing a distinct low-frequency peak in the dynamical-mobility profile. These features can be understood within approaches relying on the timescale separation between carrier and phonon dynamics, such as the transient localization scenario (TLS). However, recovering them from fully quantum dynamics has proved elusive. Using the hierarchical equations of motion (HEOM)-based approach exposed in a companion paper (arXiv:2501.05054), we study carrier transport in the one-dimensional Peierls model near the adiabatic limit. We find that the TLS approximates HEOM dynamics very well at higher temperatures and for stronger interactions. Then, the transport is predominantly phonon-assisted, and turns diffusive from the subdiffusive side well before one phonon period. In contrast, the band current dominates at moderate temperatures and interactions, relevant for transport in realistic materials. We then conclude that the super-to-subdiffusive crossover is transient, so that the diffusive motion sets in from the superdiffusive side on timescales comparable to the phonon period. The low-frequency dynamical mobility then additionally exhibits a dip at approximately one phonon frequency, and the zero-frequency peak. Our findings in this moderate regime show limitations of the TLS, and support the results of the most advanced quantum--classical simulations. We expect that the qualitative differences between HEOM and TLS dynamics would diminish for a more realistic phonon density of states.