Theory of measuring the "Luttinger-g" of a one-dimensional quantum dot

TL;DR

This paper investigates how inhomogeneities affect electron transport in one-dimensional quantum dots within Luttinger liquids, revealing non-analytic temperature behaviors and crossovers that explain recent experimental observations.

Contribution

It introduces a theoretical framework for understanding the impact of inhomogeneities on conductance in Luttinger liquid quantum dots, highlighting non-analytic temperature dependence.

Findings

Conductance peaks exhibit non-analytic temperature behavior.

Crossovers are determined by energy scales of the dot and inhomogeneity.

Results explain recent experimental findings in quantum wires and nanotubes.

Abstract

We study electron transport through a quantum dot in a Tomonaga-Luttinger liquid with an inhomogeneity induced either by a non-uniform electron interaction or by the presence of tunnel resistances of contacts. The non-analytic temperature behavior of the conductance peaks show crossovers determined by the different energy scales associated with the dot and the inhomogeneity despite the Coulomb blockade remains intact. This suggests an explanation of recent findings in semiconductor quantum wires and carbon nanotubes.