Surface nucleation critical fieldH c3(T) of type II superconductors

Abstract

Near the critical temperatureTc, the thermodynamic potential of a semi-infinite superconductor in an external magnetic field parallel to the surface can be expanded asymptotically in a power series in (1—T/Tc)1/2. In this limit the order parameter decomposes into two parts, the gauge invariant gradient of one of which is proportional to (1—T/Tc)1/2. This part satisfies asymptotically the Ginzburg Landau (GL), the generalized GL-equations and so on. The other part is of non-local nature, is asymptotically non-vanishing near the surface only and influences the boundary conditions for the former part. In general these boundary conditions can be determined to any finite order of (1—T/Tc)1/2 by solving a finite set of inhomogeneous integral equations-all with the same kernel. It turns out thatHc3(T) can be computed up to the order of (1—T/Tc)5/2 for specular and (1—T/Tc)2 for non-specular reflexion without solving the integral equations explicitly. The temperature dependence ofHc3(T)/Tc(dHc2/dT)T=Tc is given up to the orders mentioned above.