Periodicity of the giant vortex states in mesoscopic superconducting   rings
  The giant vortex states of a multiply connected superconductor, with radius comparable to the penetration depth and the coherence length, are theoretically investigated based on the nonlinear Ginzburg-Landau theory, in which the induced magnetic field by the super-currents is accurately taken into account. The solutions of Ginzburg-Landau equations are found to be actually independent of the angular momentum L in a gauge invariant point of view, provided that the hole is in the center. Different cases with the paramagnetic current, the diamagnetic current, and the coexistence of the above two, have been studied numerically. The interpretation of the L-independent solutions of Ginzburg-Landau equations is given based on the same principle of Aharonov-Bohm effect, and could be observed by Little-Parks like oscillations near the phase boundary. 
Hu Zhao, Shi-jie Yang, Shiping Feng