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Correlation Induced Inhomogeneity in Circular Quantum Dots

Amit Ghosal·A. D. Guclu·C. J. Umrigar·Denis Ullmo·Harold U. Baranger
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Abstract

Properties of the "electron gas" - in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected - change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood. For very weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and order into a Wigner crystal phase. The physics at intermediate densities, however, remains a subject of fundamental research. Here, we study the intermediate-density electron gas confined to a circular disc, where the degree of confinement can be tuned to control the density. Using accurate quantum Monte Carlo techniques, we show that the electron-electron correlation induced by an increase of the interaction first smoothly causes rings, and then angular modulation, without any signature of a sharp transition in this density range. This suggests that inhomogeneities in a confined system, which exist even without interactions, are significantly enhanced by correlations.

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Amit Ghosal, A. D. Guclu, C. J. Umrigar, Denis Ullmo, Harold U. Baranger. 2006-09-07. Correlation Induced Inhomogeneity in Circular Quantum Dots. https://doi.org/10.1038/nphys293

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