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Persistent currents in quasi-one-dimensional quantum rings: analytical treatment of the interplay of the interelectron Coulomb interaction and disorder at finite temperatures

We study persistent currents in a gas of interacting electrons confined to a quasi-one-dimensional disordered ring at arbitrary temperatures in two experimentally available regimes: at a fixed chemical potential and at a fixed number of particles. In a realistic experiment, the interelectron Coulomb interaction in a gated ring is unscreened and the potential of impurities is a smooth function of coordinates. The latter allows us to study the persistent current non-averaged over impurity realizations in a small ring. In a quasi-one-dimensional electron gas, only forward- and back-scattering processes are relevant. The forward-scattering amplitude of the Coulomb field enhances the persistent current at a fixed chemical potential but does not affect it at a fixed number of particles. The Coulomb backscattering suppresses the intrinsic disorder and enhances the persistent currents at both a fixed chemical potential and a fixed number of electrons. Increasing the number of transverse channels enhances the persistent current at strong Coulomb repulsion: . Strong Coulomb interaction cancels out oscillations over the electrochemical potential. The parity effect at a fixed number of particles is defined by the average occupation of a single channel. The non-monotonic temperature dependence of a persistent current is predicted.