Transport in a Dissipative Luttinger Liquid

TL;DR

This paper analyzes how dissipation affects electron transport in a one-dimensional Luttinger liquid with an impurity, revealing exponential suppression of conductance at low temperatures and a saturation of Friedel oscillations.

Contribution

It provides a theoretical model describing the impact of ohmic dissipation on transport properties and Friedel oscillations in a Luttinger liquid with an impurity.

Findings

Weak link becomes relevant due to dissipation, suppressing transport.

Zero-temperature current-voltage relation is exponential, I∼exp(-E₀/eV).

Finite temperature conductance decreases exponentially with temperature.

Abstract

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $\eta$ the weak link is always a relevant perturbation which suppresses transport strongly. At zero temperature the current voltage relation of the link is $I\sim \exp(-E_0/eV)$ where $E_0\sim\eta/\kappa$ and $\kappa$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $\exp(-\sqrt{{\cal C}E_0/k_BT})$. The decay of Friedel oscillation saturates for distance larger than $L_{\eta}\sim 1/\eta $ from the impurity.