Low voltage transport through a tunneling barrier in Tomonaga-Luttinger liquid constriction

TL;DR

This paper investigates how a tunneling barrier within a Tomonaga-Luttinger liquid wire affects low-voltage transport, revealing interference effects and oscillations in conductivity related to quasiparticle transitions and finite length corrections.

Contribution

It demonstrates the impact of a tunneling barrier on low-voltage transport in a Luttinger liquid, highlighting interference structures and finite length effects on conductivity.

Findings

Conductivity exhibits interference patterns due to quasiparticle transitions.

Finite length corrections cause oscillations in the voltage dependence of conductivity.

The tunneling density of states shows interference effects related to traversal times.

Abstract

As voltage decreases d.c. condctivity of a Tomonaga-Luttinger liquid wire collapses to a small value determined by the length of the wire and its contacts with the leads. In condition that voltage drop (V) mostly occurs across a tunnel barrier inside the wire the tunneling density of states and, hence, the differential conductivity are shown to exhibit an interference structure resulted from the transition of the Luttinger liquid quasiparticles into free electrons at the exits from the wire. The finite length correction to the scale-invariant $V^{2/g-2}$ dependence of the conductivity oscillates as a function of voltage with periodicities related to both rigth and left traversal times.