Transient and Sharvin resistances of Luttinger liquids

TL;DR

This paper investigates the transient conductance and contact resistance of Luttinger liquids connected to Fermi liquid electrodes, revealing a universal contact resistance involving half the quantum of conductance, using two approximate methods that match exact theory.

Contribution

It introduces a novel analysis of transient conductance to determine the Sharvin resistance in Luttinger liquids, bridging approximate methods with exact theoretical results.

Findings

Contact resistance is half the quantum of conductance in a perfect junction.

Transient measurements reveal the intrinsic contact resistance of Luttinger liquids.

Two different approximate methods agree with exact Luttinger liquid theory results.

Abstract

Although the intrinsic conductance of an interacting one-dimensional system is renormalized by the electron-electron correlations, it has been known for some time that this renormalization is washed out by the presence of the (non-interacting) electrodes to which the wire is connected. Here, we study the transient conductance of such a wire: a finite voltage bias is suddenly applied across the wire and we measure the current before it has enough time to reach its stationary value. These calculations allow us to extract the Sharvin (contact) resistance of Luttinger and Fermi liquids. In particular, we find that a perfect junction between a Fermi liquid electrode and a Luttinger liquid electrode is characterized by a contact resistance that consists of half the quantum of conductance in series with half the intrinsic resistance of an infinite Luttinger liquid. These results were obtained using two different methods: a dynamical Hartree-Fock approach and a self-consistent Boltzmann approach. Although these methods are formally approximate we find a perfect match with the exact results of Luttinger/Fermi liquid theory.