Influence of de Gennes boundary conditions on the charge distributions of the Meissner state and the single-vortex state in thin mesoscopic rings

Abstract

The vortex charge for a thin mesoscopic superconducting ring is investigated by the phenomenological Ginzburg-Landau theory with the de Gennes boundary condition. The $H\text{\ensuremath{-}}{R}_{i}$ phase diagrams for charge distributions are given for different surface extrapolation lengths ${b}_{i}$ and ${b}_{o}$ on the inner side and outer side, respectively. Five kinds of charge distribution are obtained in total. Generally, the sample is negatively charged with negative surface extrapolation lengths on each side for a surface enhancement of superconductivity, whereas the system exhibits the positive electricity with positive surface extrapolation lengths for a surface suppression of superconductivity. Specially, for the cases of $\ensuremath{-}1∕{b}_{i}>1∕{b}_{o}>0$ and $1∕{b}_{i}>\ensuremath{-}1∕{b}_{o}>0$, the sign of total charge depends on the ring size, and we find that the ring can be electronegative even if its superconductivity is suppressed. Furthermore, at the situation of $1∕{b}_{o}>1∕{b}_{i}>0$, we obtain the remarkable result that the superconducting state and the normal state cyclically appear as the field varies for a suitable size ring. As a consequence, the ring shows the electropositivity and the electroneutrality by turns with the field.