Anti-Poiseuille Flow: Increased Vortex Velocity at Superconductor Edges*

Using the time-dependent Ginzburg Landau equations we study driven vortex motion in two dimensional superconductors in the presence of a physical boundary. We observe that  when current is uniformly sourced from one and drained from the other side of a finite torus geometry, vortices start to move perpendicular to the direction of the current flow due to the applied Lorentz force, as expected.  At smaller sourced currents the lattice moves as a whole. At larger sourced current, due to the local suppression of the superconducting order parameter in the vortex cores, vortices prefer to move in separated channels. Since superconductivity is weakened at the edges of the sample, within each channel vortices will flow faster at the edges of the sample compared to the bulk. Thus, the vortex flow is opposite to the behaviour of Poiseuille's flow. Furthermore, we uncover a stick-slip motion of the vortex lattice as the sourced current is increased and vortices in the channel at the boundary break free from the Abrikosov lattice, accelerate, move past their neighbors and then slow down as another Abrikosov lattice is reestablished. So vortices in the boundary channel stick to the Abrikosov lattice then slip and then stick again at which point the stick-slip process starts over.