Persistent current and Wigner crystallization in a one dimensional quantum ring

TL;DR

This study uses Density Functional Theory to analyze how electron interactions induce Wigner crystallization and localization in a one-dimensional quantum ring, affecting persistent current behavior.

Contribution

It demonstrates the transition to a pinned Wigner crystal in a quantum ring and characterizes the phase transition using DFT-OEP calculations.

Findings

Persistent current remains constant below r_S^c=2.05

Exponential decay of current above r_S^c indicates Wigner crystal formation

Density oscillations follow a (r_S - r_S^c)^{1/2} behavior, confirming a second-order phase transition

Abstract

We use Density Functional Theory to study interacting spinless electrons on a one-dimensional quantum ring in the density range where the system undergoes Wigner crystallization. The Wigner transition leads to a drastic ``collective'' electron localization due to the Wigner crystal pinning, provided a weak impurity potential is applied. To reveal this localization we examine a persistent current in a ring penetrated by a magnetic flux. Using the DFT-OEP method we calculated the current as a function of the interaction parameter r_S. We find that in the limit of vanishing impurity potential the persistent current stays constant up to a critical value of r_S^c=2.05 but shows a drastic exponential decay for larger r_S which reflects a formation of a pinned Wigner crystal. Above r_S^c the amplitude of the electron density oscillations exactly follows the (r_S-r_S^c)^{1/2} behaviour, confirming a second-order phase transition as expected in the mean-field-type OEP approximation.