Comments on the Force on Pinned Vortices in Superconductors

The question of the nature of the force, usually referred to as the “Lorentz force” experienced by vortices in superconductors has arosen new attention in the last years. This paper contains some observations that may help understand the nature of this force, at least for stationary, pinned vortices. One observation is that the force is not proportional to the electromagnetic coupling constant, i.e. the electric charge. This points to the importance of kinematical analysis in discussing it. A second observation refers to the fact that in the London limit, kinetic energy dominates over magnetic energy in the formation energy of a vortex. We give an exact derivation of the force using the London model. We indicate that in the Ginzburg–Landau theory the same result obtains. Our derivation shows also the origin of additional forces experienced by the vortex near the sample surface.