Driving force on flowing quantum vortices in type-II superconductors with finite Ginzburg-Landau parameter

Abstract

The origin of the driving force on quantum vortices in superconductors has long been discussed. We investigate the origin of this force using the momentum flux tensor P, Maxwell stress tensor T, and numerical solutions for a flowing rectilinear vortex in the time-dependent Ginzburg-Landau (TDGL) theory for three-dimensional superconductors with finite Ginzburg-Landau parameter κ and the Maxwell equations. We calculate the hydrodynamic force Fhydro(C) and magnetic Lorentz force Fmag(C) respectively using the contour integral of P and T along a closed path that winds around the vortex line. The calculations show that neither Fhydro(C) nor Fmag(C) reaches the full magnitude of the driving force. However, when the path C is farther than the penetration depth from the vortex line and hence the energy dissipation is negligible on C, the sum of the two forces becomes independent of the choice of C and accounts for the full magnitude of the driving force on the vortex. We demonstrate the applicability of this result to a flowing vortex described in the generalized or modified version of the TDGL equation and to a pinned vortex. We then discuss the driving force on the Pearl vortex in two-dimensional superconductors and a curved vortex line in three-dimensional superconductors. We propose an experiment that locally probes the magnetic field with a pinned vortex to verify our results that the contribution of the magnetic pressure (Lorentz force) to the total driving force on the vortex is less than half.

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