Abstract
Vortex states in mesoscopic superconducting rings are investigated by the phenomenological Ginzburg-Landau theory in the presence of an externally applied magnetic field. We obtain the cylindrical symmetric giant vortex states (GVS) by solving an eigenvalue problem and minimizing the system free energy. Ground state transitions between GVS and multivortex states are found as system dimensions and magnetic field vary. Metastability and negative flux jump associated with quantum size effect and proximity effect are revealed. Also, We find that the superconducting state and the normal state can alternately appear with external field increasing.
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