Superconducting state in a mesoscopic segment ring

In this paper we study the formation of vortices in a mesoscopic superconducting segment ring. We evaluate the magnetization, superconducting to normal magnetic field transition and the superconductor density of electrons. Our results point out that, as we reduce the superconducting segment width, remaining its area constant, both the first and third critical fields increases. Also, the third critical field exhibits a typical behavior as function of the angular width Θ of the segment ring, namely, the curve H C 3 ( Θ ) decreases monotonically with increasing the angle width and diverges in the limit Θ → 0 . In addition, we have found an analytical expression from the magnetization as a function of the segment width.