Nonequilibrium dynamics of the Holstein polaron driven by external electric field

TL;DR

This study investigates the nonequilibrium behavior of a Holstein polaron in one dimension under a constant electric field, revealing how electron-phonon interactions influence current, oscillations, and polaron dynamics.

Contribution

It provides a comprehensive quantum-mechanical analysis of polaron dynamics under electric fields, including analytic steady-state current expressions and detailed polaron shape evolution.

Findings

Weak EP coupling shows damped Bloch oscillations.

Analytic steady state current expression derived.

Strong coupling maintains weakly damped BO at high fields.

Abstract

This work represents a fundamental study of a Holstein polaron in one dimension driven away from the ground state by a constant electric field. Taking fully into account quantum effects we follow the time-evolution of the system from its ground state as the constant electric field is switched on at t = 0, until it reaches a steady state. At weak electron phonon coupling (EP) the system experiences damped Bloch oscillations (BO) characteristic for noninteracting electron band. An analytic expression of the steady state current is proposed in terms of weak EP coupling and large electric field. For moderate values of EP coupling the oscillations are almost critically damped and the system reaches the steady state after a short time. In the strong coupling limit weakly damped BO, consistent with nearly adiabatic evolution within the polaron band, persist up to extremely large electric fields. A traveling polaron under the influence of the electric field leaves behind a trail of phonon excitations absorbing the excess energy gained from the electric field. The shape of the traveling polaron is investigated in details.