Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

TL;DR

This paper investigates the chemical potential oscillations in a one-dimensional quantum dot using Luttinger liquid theory, highlighting how Friedel and Wigner oscillations reveal different physical phenomena and spin states.

Contribution

It provides a detailed analysis of chemical potential oscillations in a quantum dot, distinguishing Friedel and Wigner oscillations and their sensitivity to spin states within a Luttinger liquid framework.

Findings

Friedel oscillations are sensitive to excited spin states.

Wigner oscillations are influenced by electron-electron interactions.

The study compares linear and non-linear transport regimes.

Abstract

We evaluate the chemical potential of a one-dimensional quantum dot, coupled to an atomic force microscope tip. The dot is described within the Luttinger liquid framework and the conductance peaks positions as a function of the tip location are calculated in the linear and non-linear transport regimes for an arbitrary number of particles. The differences between the chemical potential oscillations induced by Friedel and Wigner terms are carefully analyzed in the whole range of interaction strength. It is shown that Friedel oscillations, differently from the Wigner ones, are sensitive probes to detect excited spin states and collective spin density waves involved in the transport.