Berlin 2008 – scientific programme
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SYEC: Symposium Exact-exchange and hybrid functionals meet quasiparticle energy calculations
SYEC 2: Exact-exchange and hybrid functionals meet quasiparticle energy calculations II
SYEC 2.6: Talk
Thursday, February 28, 2008, 15:15–15:30, A 053
Wigner crystallization in exact exchange theory: calculation of the persistent current in a quantum ring — •Marc Siegmund and Oleg Pankratov — Lehrstuhl für Theoretische Festkörperphysik, Universität Erlangen-Nürnberg, Staudtstr. 7/B2, 91058 Erlangen
A pinned Wigner crystal is a correlated many-body state with electrons localized at discrete lattice sites. At low electron densities such a crystalline state supersedes the Fermi liquid state as the Coulomb repulsion dominates over the kinetic energy. The electron crystal can be pinned by the arbitrarily weak localized potential which would have no effect on the Fermi liquid state. Hence the Wigner crystallization should result in a drastic “collective” localization of electrons provided a pinning potential is applied.
We use the DFT-OEP method (in KLI approximation) to calculate the electron persistent current induced by magnetic flux through the quantum ring. The current is calculated as a function of the interaction parameter rS in the density range where the system undergoes Wigner transition. At high densities (small rS) the current is independent of rS whereas below some critical density the current drops exponentially indicating a transition to the localized Wigner state. We find the critical rSc≈ 2.05.
The amplitude of the electron density oscillations shows a clear square root dependence on rS−rSc, indicating a second-order character of the phase transition. This is a natural consequence of the mean-field-type DFT-OEP approach.