Current distribution and vortex-vortex interaction in a superconducting film of finite thickness

The current distribution due to a single vortex in a superconducting film of finite thickness is calculated, based on the London model. At large distances from the vortex core, the current density on the surface of the superconductor was found to follow the 1/r(2) law which has a simple expression, J(s)(r, 0) approximate to phi(0)[coth(d/lambda) + csch (d/lambda)]/2 pi mu(0) lambda r(2). We also find that the interaction energy between two vortices has the form, U-int(r/(12)) phi(0)(2)[H-0(r(12)/lambda') - Y-0(r(12)/lambda l)], when the film is not too thick and at large distances between two vortices. This potential differs from Pearl's result by the new effective penetration depth lambda' = 2 lambda coth (d/lambda).