Persistent currents in coupled mesoscopic rings

TL;DR

This paper analytically investigates persistent currents in coupled mesoscopic rings connected to an electron reservoir, revealing generalized parity effects and conditions for opposite currents in rings of unequal sizes.

Contribution

It provides analytical expressions for persistent currents in coupled rings and generalizes known effects to this more complex system.

Findings

Parity effects are generalized for coupled rings.

Opposite currents can occur in rings of unequal size.

Analytical formulas for current densities are derived.

Abstract

We have analysed the nature of persistent currents in open coupled mesoscopic rings. Our system is comprised of two ideal loops connected to an electron reservoir. We have obtained analytical expressions for the persistent current densities in two rings in the presence of a magnetic field. We show that the known even-odd parity effects in isolated single loops have to be generalised for the case of coupled rings. We also show that when the two rings have unequal circumferences, it is possible to observe opposite currents (diamagnetic or paramagnetic) in the two rings for a given Fermi level.