Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

TL;DR

This paper investigates how resistive regions affect the conductance of interacting quantum wires and their junctions, revealing that resistance can lead to incoherent transport and that conductance depends on system parameters in complex ways.

Contribution

It introduces a model combining bosonization and dissipation to analyze conductance in resistive Tomonaga-Luttinger liquids and their junctions, highlighting new dependencies on system parameters.

Findings

Resistances add in series to contact resistance for single wires.

Conductance in junctions depends on the Luttinger parameter K_W for certain configurations.

Numerical simulations show charge pulse behavior varies with resistive and interacting regions.

Abstract

We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h/e^2 for spinless electrons, and the total resistance is independent of the Luttinger parameter K_W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K_W for one family but is independent of K_W for the other family, regardless of the resistances present in the system.