AFM probe for the signatures of Wigner correlations in the conductance of a one-dimensional quantum dot

TL;DR

This paper investigates how an AFM probe can detect Wigner correlations in a one-dimensional quantum dot by analyzing conductance oscillations and beating patterns, revealing signatures of Wigner molecules and their dependence on interactions.

Contribution

It introduces a method to identify Wigner correlations in quantum dots through conductance measurements influenced by an AFM probe within a Luttinger liquid framework.

Findings

Conductance peak position and height oscillate with tip position.

Beating patterns in conductance are linked to electron density oscillations.

Wigner effects are enhanced at strong interactions, while Friedel oscillations remain robust.

Abstract

The transport properties of an interacting one-dimensional quantum dot capacitively coupled to an atomic force microscope probe are investigated. The dot is described within a Luttinger liquid framework which captures both Friedel and Wigner oscillations. In the linear regime, we demonstrate that both the conductance peak position and height oscillate as the tip is scanned along the dot. A pronounced beating pattern in the conductance maximum is observed, connected to the oscillations of the electron density. Signatures of the effects induced by a Wigner molecule are clearly identified and their stability against the strength of Coulomb interactions are analyzed. While the oscillations of the peak position due to Wigner get enhanced at strong interactions, the peak height modulations are suppressed as interactions grow. Oscillations due to Friedel, on the other hand, are robust against interaction.