Vortex state in a mesoscopic flat disk with rough surface

In this paper we study some superconducting properties of a flat disk by taking into account the roughness of the surface. Also, the sample is surrounded by a thin layer of a metallic material and submitted to and external magnetic field applied perpendicular to its plane. The boundary condition is taking into account via the de Gennes extrapolation length b. We evaluate the Gibbs free energy, magnetization, vorticity, the first and second critical thermodynamical fields as a function of the external magnetic field and b parameter. We also evaluate the first critical field as a function of the surface rugosity.