Mesoscopic persistent current in small rings

Small normal-metal rings threaded by a constant magnetic flux have been shown to carry a mesoscopic persistent current at low temperatures. The current is a few-electron effect and its sign and amplitude depend on the microscopic configuration of disorder. Assuming a Gaussian current distribution, we characterize the effect by three quantities, the rms or typical total current I^typ=〈I²〉_D^1/2, the average current I^av=〈I〉_D, and the typical single-level current i^typ=〈i²〉_D^1/2. Specifically, we review and extend the analytical calculations for the typical total and single-level currents focusing on the case of noninteracting electrons in disordered rings in the regime of diffusive transport. We calculate and discuss those current-current correlation functions that describe the dependences of the persistent current on filling, flux, and disorder configuration. Only the single-electron contribution discussed in this paper is known to contribute to the first, φ₀-periodic harmonic of the total current in a single ring. The second harmonic also contains an interaction-induced contribution proposed by Ambegaokar and Eckern that survives the disorder average. The Thouless correlation energy E_c is the characteristic energy scale for the amplitude of the total current and its dependences on filling, temperature, and inelastic scattering. The persistent current is sensitive to changing the position of a single impurity. We compare our results with the recent single-ring experiment by Chandrasekhar et al.