Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model

TL;DR

This paper investigates how coupling to optical phonons causes the breakdown of quantized Thouless charge pumping in the Rice-Mele-Holstein model, revealing resonance conditions and parameter regimes where topological transport fails or becomes non-quantized.

Contribution

It introduces a semi-classical Ehrenfest approach to study phonon effects on topological charge pumping, demonstrating phonon-induced breakdown and regimes of non-quantized transport.

Findings

Quantized charge pumping breaks down at phonon resonance conditions.

Electron-phonon coupling modifies the effective pumping path.

Phonons eliminate the potential staggering needed for pumping in large coupling regimes.

Abstract

Adiabatic and periodic variation of the lattice parameters can make it possible to transport charge through a system even without net external electric or magnetic fields, known as Thouless charge pumping. The amount of charge pumped in a cycle is quantized and entirely determined by the system's topology, which is robust against perturbations such as disorder and interactions. However, coupling to the environment may play a vital role in topological transport in many-body systems. We study the topological Thouless pumping, where the charge carriers interact with local optical phonons. The semi-classical multi-trajectory Ehrenfest method is employed to treat the phonon trajectories classically and charge carriers quantum mechanically. We find a breakdown of the quantized charge transport in the presence of phonons. It happens for any finite electron-phonon coupling strength at the resonance condition when the pumping frequency matches the phonon frequency, and it takes finite phonon coupling strength away from the resonance. Moreover, there exist parameter regimes with non-quantized negative and positive charge transport. The modified effective pumping path due to electron-phonon coupling accurately explains the underlying physics. In the large coupling regime where the pumping disappears, the phonons are found to eliminate the staggering of the onsite potentials, which is necessary for the pumping protocol. Finally, we present a stability diagram of quantized pumping as a function of time period of pumping and phonon coupling strength.