Transport properties of a two-lead Luttinger liquid junction out of equilibrium: fermionic representation

TL;DR

This paper calculates the electrical current through a junction of interacting quantum wires out of equilibrium using fermionic representation, deriving renormalization group equations for conductance as a function of voltage and other scales.

Contribution

It introduces a fermionic approach to analyze out-of-equilibrium transport in Luttinger liquid junctions and derives RG equations for conductance considering infinite-order interactions.

Findings

Identifies two fixed points with power-law conductance behavior.

Derives RG equations for conductance as a function of voltage and temperature.

Provides a framework for understanding crossover regimes in quantum wire junctions.

Abstract

The electrical current through an arbitrary junction connecting quantum wires of spinless interacting fermions is calculated in fermionic representation. The wires are adiabatically attached to two reservoirs at chemical potentials differing by the applied voltage bias. The relevant scale-dependent contributions in perturbation theory in the interaction up to infinite order are evaluated and summed up. The result allows one to construct renormalization group equations for the conductance as a function of voltage (or temperature, wire length). There are two fixed points at which the conductance follows a power law in terms of a scaling variable $\Lambda$, which equals the bias voltage $V$, if $V$ is the largest energy scale compared to temperature $T$ and inverse wire length $L^{-1}$, and interpolates between these quantities in the crossover regimes.