Tunneling through a barrier in Tomonaga-Luttinger liquid connected to reservoirs

TL;DR

This paper investigates how a barrier affects electrical conductance in a finite-length Tomonaga-Luttinger liquid connected to reservoirs, analyzing the influence of voltage, temperature, and wire length.

Contribution

It derives an effective action for the phase variable at the barrier, incorporating spatially varying electric fields and barrier location effects.

Findings

Conductance depends on total voltage drop in the d.c. limit.

Temperature and wire length influence conductance through RG flow crossovers.

Barrier position affects the conductance behavior.

Abstract

The transport through a barrier is studied for a Tomonaga-Luttinger liquid of finite length connected to reservoirs. An effective action for the phase variable at the barrier is derived for spatially varying electric field. In the d.c. limit only the total voltage drop between the left and right reservoirs appears in the action. We discuss crossovers of the renormalization group flow and hence of the temperature and wire length dependence of the conductance, taking into account the location of the barrier.