Current-carrying ground states in mesoscopic and macroscopic systems

Michael R. Geller
1996 Physical Review B (Condensed Matter)  
We extend a theorem of Bloch, which concerns the net orbital current carried by an interacting electron system in equilibrium, to include mesoscopic effects. We obtain a rigorous upper bound to the allowed ground-state current in a ring or disc, for an interacting electron system in the presence of static but otherwise arbitrary electric and magnetic fields. We also investigate the effects of spin-orbit and current-current interactions on the upper bound. Current-current interactions, caused by
more » ... ractions, caused by the magnetic field produced at a point r by a moving electron at r, are found to reduce the upper bound by an amount that is determined by the self-inductance of the system. A solvable model of an electron system that includes current-current interactions is shown to realize our upper bound, and the upper bound is compared with measurements of the persistent current in a single ring.
doi:10.1103/physrevb.53.9550 pmid:9982497 fatcat:nq2ey4srhfaxjkwqhpuug4v46a