From Tomonaga-Luttinger to Fermi liquid in transport through a tunneling barrier

TL;DR

This paper investigates how finite wire length causes a crossover from Tomonaga-Luttinger to Fermi liquid behavior in tunneling conductance, revealing oscillations and corrections at higher voltages.

Contribution

It introduces a detailed analysis of conductance behavior considering finite length effects and voltage drop conditions, providing new insights into crossover phenomena.

Findings

Finite length induces a crossover from Luttinger to Fermi liquid behavior.

Conductance exhibits oscillations related to traversal times at high voltages.

Finite length effects add slowly decaying corrections to conductance scaling.

Abstract

Finite length of a one channel wire results in crossover from a Tomonaga-Luttinger to Fermi liquid behavior with lowering energy scale. In condition that voltage drop $(V)$ mostly occurs across a tunnel barrier inside the wire we found coefficients of temperature/voltage expansion of low energy conductance as a function of constant of interaction, right and left traversal times. At higher voltage the finite length contribution exhibits oscillations related to both traversal times and becomes a slowly decaying correction to the scale-invariant $V^{1/g-1}$ dependence of the conductance.