Effect of eccentricity and boundary conditions on the edge superconducting states in mesoscopic rings

It is considered a mesoscopic superconductor ring in the presence of an external magnetic field applied in the direction perpendicular to the ring plane. The internal and external edges have circular form but they are excentric, the excentricity being more less than the difference between the edge radii. Special attention is devoted to the influence of the different materials, contacting the inner and external edges of the superconductor, on the features of the phase diagram and of regions where the paramagnetic Meissner effect exists. In order to discuss the effect of the eccentricity on the phase diagram, the Green theorem was adapted to find the correction to the eigenstates of the concentric problem. It is demonstrated that such correction depends cuadratically on the excentricity and it is negative, which leads to the following features: (i) The quasiperiod of the characteristic oscillations of the phase diagram is altered in such way, that the transitions between different vortex states occur at smaller values of the magnetic fields. (ii) For a given value of the temperature, there is an increasing of the range of values of magnetic fields for which the superconducting states associated to the presence of the edges are observed.