Coulomb interaction and persistent currents in ensembles of mesoscopic metal rings
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The average persistent current in an ensemble of mesoscopic metal rings at fixed chemical potential threaded by a magnetic flux in the diffusive regime is related to the presence of a component of the one-electron effective self-energy, which is odd with respect to the electron velocity. In a noninteracting model, the ''velocity-odd'' component of the self-energy, calculated within the self-consistent Born approximation, is found to be exponentially small. Hence, the average persistent current is also exponentially small. When the Coulomb interaction between electrons is included, a finite velocity-odd component of the self-energy is obtained. The microscopic reason for this is the enhancement of the average classical electrostatic energy of interaction between two electrons with almost opposite velocities. We show that the recent theory of Ambegaokar and Eckern can be reformulated in terms of a velocity-odd self-energy, and their results are reproduced. A simple model is then presented, which exhibits the main qualitative features of their result in an elementary way. Finally, the assumption that all rings have the same chemical potential is examined. It is shown that the error involved in this approximation is parametrically small for three-dimensional rings, scaling as the inverse of the volume of the ring.
Phys. Rev. B 50, 7668-7679 (1994)