Finite-bias transport through the interacting resonant level model coupled to a phonon mode -- a functional renormalization group study

TL;DR

This study uses a functional renormalization group approach to analyze how fermion-fermion and fermion-boson interactions influence transport properties in a quantum dot system coupled to a phonon mode, revealing effects like Franck-Condon blockade and negative differential conductance.

Contribution

It provides a nonperturbative analysis of the interacting resonant level model with phonon coupling, highlighting the interplay of interactions on low-energy scales and transport characteristics.

Findings

Fermion-boson interaction causes Franck-Condon blockade and phonon sidebands.

Fermion-fermion interaction leads to negative differential conductance.

The low-order FRG approach has limitations related to current conservation.

Abstract

We study the nonlinear steady-state transport of spinless fermions through a quantum dot with a local two-particle interaction. The dot degree of freedom is in addition coupled to a phonon mode. This setup combines the nonequilibrium physics of the interacting resonant level model and that of the Anderson-Holstein model. The fermion-fermion interaction defies a perturbative treatment. We mainly focus on the antiadiabatic limit, with the phonon frequency being larger than the lead-dot tunneling rate. In this regime also the fermion-boson coupling cannot be treated perturbatively. Our goal is two-fold. We investigate the competing roles of the fermion-fermion and fermion-boson interactions on the emergent low-energy scale $T_{\rm K}$ and show how $T_{\rm K}$ manifests in the transport coefficients as well as the current-voltage characteristics. For small to intermediate interactions, the latter is in addition directly affected by both interactions independently. With increasing fermion-boson interaction the Franck-Condon blockade suppresses the current at small voltages and the emission of phonons leads to shoulders or steps at multiples of the phonon frequency, while the local fermion-fermion interaction implies a negative differential conductance at voltages larger than $T_{\rm K}$. We, in addition, use the model to investigate the limitations of our low-order truncated functional renormalization group approach on the Keldysh contour. In particular, we quantify the role of the broken current conservation.