Persistent current and Wigner crystallization in a one dimensional quantum ring

Details Persistent current and Wigner crystallization in a one dimensional quantum ring Persistent current and Wigner crystallization in a one dimensional quantum ring

2007-11-19

arxiv.org/abs/0711.2937v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, 5 figures

Scientific paper

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.

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