Mesoscopic ring in a magnetic field: Reactive and dissipative response

The response of a normal-metal ring threaded by a magnetic field and coupled to a dissipative external bath is studied via the Kubo formalism. Unlike in a wire, the diamagnetic contribution to the induced current in a multiply connected geometry is not completely canceled by the paramagnetic term, resulting in a persistent current in the ring. We find a nonzero reactive response Imσ which is a periodic function of the flux through the ring with period ${\phi }_0$=hc/e for a single ring, but a period of ${\phi }_0$/2 for an array of disconnected rings. The residual diamagnetic effects also contribute to intraband scattering in the ring. It is shown that the minimum in the dissipative response Reσ for zero flux seen in experiments is obtained upon a proper inclusion of intraband scattering (often omitted) in addition to the usual interband scattering. A new regime appears in the response functions where quantum size effects, i.e., a sensitivity to the discreteness of the energy levels, are probed when the broadening of levels γ and the temperature T are much less than the typical spacing between levels δE.