title: Exact-exchange spin-density functional theory of Wigner localization and phase transitions in quantum rings.
abstract: We apply exact-exchange spin-density functional theory in the Krieger-Li-Iafrate approximation to interacting electrons in quantum rings of different widths. The rings are threaded by a magnetic flux that induces a persistent current. A weak space and spin symmetry breaking potential is introduced to allow for localized solutions. As the electron-electron interaction strength described by the dimensionless parameter r(S) is increased, we observe-at a fixed spin magnetic moment-the subsequent transition of both spin sub-systems from the Fermi liquid to the Wigner crystal state. A dramatic signature of Wigner crystallization is that the persistent current drops sharply with increasing r(S). We observe simultaneously the emergence of pronounced oscillations in the spin-resolved densities and in the electron localization functions indicating a spatial electron localization showing ferrimagnetic order after both spin sub-systems have undergone the Wigner crystallization. The critical r(S)(c) at the transition point is substantially smaller than in a fully spin-polarized system and decreases further with decreasing ring width. Relaxing the constraint of a fixed spin magnetic moment, we find that on increasing r(S) the stable phase changes from an unpolarized Fermi liquid to an antiferromagnetic Wigner crystal and finally to a fully polarized Fermi liquid.
authors.affiliation: Lehrstuhl für Theoretische Festkörperphysik, Universität Erlangen-Nürnberg, Staudtstrasse 7 B2, D-91058 Erlangen, Germany. thorsten.arnold@physik.uni-erlangen.de
authors.forename: Thorsten
authors.initials: T
authors.lastname: Arnold
authors.forename: Marc
authors.initials: M
authors.lastname: Siegmund
authors.forename: Oleg
authors.initials: O
authors.lastname: Pankratov
mesh_terms: D004583:Electrons; D008280:Magnetics; D008962:Models, Theoretical; D044367:Phase Transition; D011789:Quantum Theory; D012996:Solutions; D013113:Spin Labels; D013696:Temperature
chemical_list: D012996:Solutions; D013113:Spin Labels