Quantum rings for beginners: energy spectra and persistent currents

By S. Viefers, Pekka Koskinen, P. Deo, M. Manninen. 2003

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Abstract Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation–vibration spectrum of a “Wigner molecule” of “localized” electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the “rigid rotation” of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Φ 0 . For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Φ 0 first to Φ 0 /2 and eventually to Φ 0 / N when the ring gets narrower.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/5e16e2a34e17fb9b4a065d008e8d53bc4f35dabd