Conductance of a Mott Quantum Wire

TL;DR

This paper investigates electron transport in a one-dimensional Mott quantum wire, revealing conductance jumps at the Mott gap edge and analyzing the effects of potential strength and Umklapp scattering.

Contribution

It provides a detailed analysis of conductance behavior in a Mott quantum wire, highlighting the discontinuous jump at the gap edge and the absence of perturbative corrections away from half-filling.

Findings

Conductance jumps from zero to 2e^2/h at the Mott gap edge.

Optical conductivity varies continuously, unlike conductance.

Weak potential case shows no perturbative correction away from half-filling.

Abstract

We consider transport through a one-dimensional conductor subject to an external periodic potential and connected to non-interacting leads (a "Mott quantum wire"). For the case of a strong periodic potential, the conductance is shown to jump from zero, for the chemical potential lying within the Mott-Hubbard gap, to the non-interacting value of 2e^2/h, as soon as the chemical potential crosses the gap edge. This behavior is strikingly different from that of an optical conductivity, which varies continuously with the carrier concentration. For the case of a weak potential, the perturbative correction to the conductance due to Umklapp scattering is absent away from half-filling.