Fractional periodicity and magnetism of extended quantum rings

TL;DR

This paper investigates the magnetic properties and persistent currents in extended quantum rings, introducing an effective rigid-rotator model that explains ferromagnetic transitions and aligns lattice and continuum models.

Contribution

It develops an effective rigid-rotator description for quantum rings, linking ferromagnetic states with persistent current behavior and bridging lattice and continuum models.

Findings

Ferromagnetic solutions occur without Zeeman coupling.

High correspondence (97-98%) between lattice and continuum models after rigid rotation onset.

Criteria for the transition to effective rigid rotation are established.

Abstract

The magnetic properties and nature of the persistent current in small flux-penetrated $t-t'-U$ rings are investigated. An effective rigid-rotator description is formulated for this system, which coincides with a transition to a ferromagnetic state in the model. The criteria for the onset of effective rigid rotation is given. The model is used to understand continuum model ground-state solutions for a 2D few-particle hard-wall quantum dot, where ferromagnetic solutions are found even without the Zeeman coupling to spin. After the onset of effective rigid rotation, a 97--98% correspondence can be determined between the lattice model and continuum model eigenstate results.