Dynamical Coulomb Blockade in an interacting 1D system coupled to an arbitrary environment

TL;DR

This paper analyzes out-of-equilibrium transport in a 1D interacting system coupled to an arbitrary environment, deriving formal expressions for current and noise, and exploring effects of environmental impedance on conductance and noise.

Contribution

It provides a comprehensive theoretical framework for calculating transport properties in a Tomonaga-Luttinger liquid with environmental coupling, including explicit results for harmonic oscillator environments.

Findings

Duality between weak and strong backscattering regimes breaks down at finite frequency.

Explicit formulas for current and noise at arbitrary voltages, temperatures, and impedance.

Environmental impedance significantly influences nonlinear conductance and noise.

Abstract

We study the out-of-equilibrium transport in a Tomonaga-Luttinger liquid containing a weak or a tunneling barrier coupled to an arbitrary electromagnetic environment. This applies as well to a coherent one-channel non-interacting conductor with a transmission coefficient close to one or to zero. We derive formal expressions for the current and finite-frequency (FF) noise at arbitrary voltages, temperatures and frequency-dependent impedance $Z(\omega)$ in the regimes of weak and strong backscattering. We show that these two regimes are no longer related by duality at finite frequency. We then carry explicit computations of the nonlinear conductance and FF noise when $Z(\omega)$ describes an harmonic oscillator such as a LC circuit or a cavity.