Dependence of the charge distribution on the size of thin mesoscopic rings

The influence of the size of thin mesoscopic superconducting ring on the charge distribution is investigated by the phenomenological Ginzburg-Landau theory. For a giant vortex state of angular quantum number L, we find that three physical quantities, that is, the critical radius Rcr which corresponds to a maximum upper nucleation field Hnuc,u for a disk sample, the critical outer radius Ro,cr that gives a maximum value of the minimum inner radius Ri,min beyond which the vortex state L can possibly be excited, and the critical inner radius Ri,cr which leads to a maximum upper nucleation field Hnuc,u in comparison with other inner radii for a fixed outer radius Ro, determine the feature of boundaries of the phase diagram for charge distributions.