Nonlocal Ginzburg-Landau Equations¹

Real time Gor'kov equations and the accompanying electric current expression in terms of the retarded Green's functions are established at finite temperatures with the aid of the Closed-Time-Path-Green's-Function formalism. The fluctuation-dissipation theorem then helps us to obtain nonlocal G-L equations near T_c which reduces to the conventional G-L equations in the local limit. The kernel containing nonlocal effects in our equations has an asymptotic behavior k^-2 for $\text{k}\,\rightarrow \,\infty$ and is, therefore, quite different from the BCS kernel. This novel kernel leads naturally to reversal of the magnetic field in the neighborhood of a vortex in type II/1 superconductors.