Regensburg 2007 – scientific programme
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HL: Fachverband Halbleiterphysik
HL 43: Theory of electronic structure
HL 43.4: Talk
Thursday, March 29, 2007, 14:45–15:00, H14
Electron Localization Function, persistent current and Wigner crystal phase in a one-dimensional quantum ring — •Marc Siegmund and Oleg Pankratov — Lst. für Theoretische Festkörperphysik, Universität Erlangen-Nürnberg, Staudtstr.7, 91058 Erlangen
Due to the absence of long-range order in one-dimensional (1D) systems, the existence of a 1D Wigner crystal has been a long debated subject. It was shown [1] that despite the strong fluctuations, already a small pinning potential can stabilize the crystal phase at moderate electron densities. We confirm the existence of a 1D Wigner phase via studying a persistent current in a one-dimensional quantum ring with a single Gaussian impurity. The current is induced by a magnetic flux penetrating the ring. To calculate the current we use Density Functional Theory with OEP approximation for exchange effects. The Wigner crystallization manifests itself as a drastic decrease of the current at a critical value rSc. In the limit of a vanishing impurity potential we find a sharp drop of the current, whereas for a finite potential strength the transition is smooth. We interpret the observed behaviour as a pinning of a Wigner crystal phase at rSc≈ 2.2 (for 0.3 of the flux quantum). This interpretation is supported by the calculation of the Electron Localization Function [2]. The latter shows the delocalized electron distribution for rS<rSc, which drastically changes reflecting a strong localization of periodically arranged electrons at rS>rSc.
[1] L.I. Glazman et al., Phys. Rev. B 45, 8454 (1992)
[2] A.D. Becke and K.E. Edgecombe , J. Chem. Phys. 92, 5397 (1990)