Charging of a quantum dot coupled to Luttinger liquid leads

TL;DR

This paper proposes an experimental setup to measure the Luttinger liquid parameter K in quantum wires by combining resonant transport and charge measurements on a quantum dot, providing a test for Luttinger liquid behavior.

Contribution

It introduces a novel method to verify Luttinger liquid theory through two independent measurements of the interaction parameter K.

Findings

Two measurement methods for K can be used to test Luttinger liquid behavior.

Consistency between the two measurements supports the Luttinger liquid paradigm.

The setup enables experimental validation of theoretical predictions in one-dimensional correlated systems.

Abstract

Luttinger liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter K. We suggest a setup to study Luttinger liquid behavior in quantum wires which allows to determine K from two independent measurements: resonant transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two measured values of K for a single probe would provide strong experimental evidence for the Luttinger liquid paradigm.