Current-Carrying Ground States in Mesoscopic and Macroscopic Systems

TL;DR

This paper extends Bloch's theorem to mesoscopic systems, providing a rigorous upper bound on ground-state currents in interacting electron systems under various fields, and compares theoretical bounds with experimental data.

Contribution

It introduces a generalized upper bound on ground-state currents in mesoscopic systems, accounting for spin-orbit and current-current interactions, and validates it with a solvable model and experiments.

Findings

Derived a rigorous upper bound on persistent currents in mesoscopic rings.

Current-current interactions reduce the maximum allowed current based on self-inductance.

The model confirms the theoretical upper bound aligns with experimental measurements.

Abstract

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 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.