Surface Effects in the Mixed Superconducting State

Measurements of the critical transport current above $H_{c1\mathrm{}}$ in a variety of ${\mathrm{Pb}}_{0.95}$ ${\mathrm{Tl}}_{0.05}$ samples reveal that the surface can support a large transport current in the mixed state when the magnetic field vector is aligned with the surface. When a geometry is chosen so that the magnetic field vector can be aligned with a single surface (e.g., a cylinder of triangular cross section), the critical currents of opposite polarities differ by over a factor of 3 when the magnetic field vector is parallel to a surface plane; partial rectification is thus observed. The larger critical current is always in a direction that indicates that magnetic flux crosses out of the surface of a type-II superconductor more easily than into the surface. The "anomalous peak effect" (a maximum in the critical current just below $H_{c2\mathrm{}}$) is observed in annealed samples and is identified with the strength of the Saint-James-de Gennes surface film below $H_{c2\mathrm{}}$ because of the manner in which it is affected by a thin surface film of copper. The critical-transport-current results suggest that two separate mechanisms contribute to the surface transport current in the mixed state. One of these mechanisms is identified with the Saint-James-de Gennes surface film below $H_{c2\mathrm{}}$; the second is tentatively associated with a bulk penetration depth. We measured a mixed-state resistivity and separated the contributions from the surface and the bulk. The bulk mixed-state resistivity is found to be independent of the density of bulk defects.