Persistent currents in mesoscopic rings, conductance, and boundary conditions.

Abstract

The persistent current of a mesoscopic ring pierced by a magnetic flux and the conductance of the same sample in an open geometry are two quantities that measure the sensitivity of the spectrum to the boundary conditions. We study the content in harmonics of the variation with the flux of the energy of a single level. This content is different from the harmonic content of the total energy. We find that there is a well-defined relation between the harmonic content of the persistent current and the correlation function of these currents on an energy range equal to the Thouless correlation energy ${\mathit{E}}_{\mathit{c}}$=\ensuremath{\Elzxh}D/${\mathit{L}}^{2}$. These results provide a self-consistency check between the various analytical and numerical results relating the conductance to the single level and total flux dependence of the persistent currents.