Coherence and persistent currents in mesoscopic rings

We calculate, to first order in the screened electron-electron interaction, the grand potential and the equilibrium current in a mesoscopic normal-metal ring threaded by a magnetic flux. The average current in an ensemble of such rings is found to be periodic in the flux with period h/2e, and to be given at zero temperature in order of magnitude by I∼${\mathit{ev}}_{\mathit{F}}$l/${\mathit{L}}^2$, where l is the mean free path and L the circumference of the ring. Interference between time-reversed paths, as in the theory of weak localization, is the crucial ingredient. The effect decreases exponentially with temperature on a scale determined by the coherence energy ∼hD/${\mathit{L}}^2$, where D is the electronic diffusion constant. The results are in good agreement with recent measurements.