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Correlation-induced inhomogeneity in circular quantum dots

Nature Physics volume 2, pages 336–340 (2006)Cite this article

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 understood1. 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 research2,3,4,5,6,7,8. 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 techniques9, 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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Figure 1: Electron density, n(r), for the ground state of an N=20 circular quantum dot (L=0, S=0).
Figure 2: Pair density of the circular quantum dot with an up-electron fixed on the outer ring.
Figure 3: Ground-state energy.

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Acknowledgements

This work was supported in part by the NSF (grants DMR-0506953 and DMR-0205328). A.G. was supported in part by the funds from the David Saxon chair at UCLA.

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Author notes

  1. Amit Ghosal

    Present address: Physics Department, University of California, Los Angeles, California, 90095-1547, USA

Authors and Affiliations

  1. Department of Physics, Duke University, Durham, North Carolina 27708-0305, USA

    Amit Ghosal, Denis Ullmo & Harold U. Baranger

  2. Theory Center and Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

    A. D. Güçlü & C. J. Umrigar

  3. CNRS; Univ. Paris-Sud, LPTMS UMR 8626, 91405 Orsay Cedex, France

    Denis Ullmo

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  1. Amit Ghosal
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  2. A. D. Güçlü
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Corresponding authors

Correspondence to Amit Ghosal or Harold U. Baranger.

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Ghosal, A., Güçlü, A., Umrigar, C. et al. Correlation-induced inhomogeneity in circular quantum dots. Nature Phys 2, 336–340 (2006). https://doi.org/10.1038/nphys293

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