Thermodynamics of the polaron master equation at finite bias

TL;DR

This paper develops a thermodynamically consistent master equation for a double quantum dot system coupled to phonons and electronic leads, revealing transport signatures and fluctuation relations in nonequilibrium conditions.

Contribution

It introduces a non-perturbative polaron-transformed master equation applicable to finite and infinite phonon modes, with new insights into transport and fluctuation theorems.

Findings

Transport spectroscopy reveals phonon frequencies and Franck-Condon blockade signatures.

Current oscillations occur due to electron-phonon coupling at finite bias.

Full fluctuation theorem matches entropy production in the system.

Abstract

We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system.