Local superfluid densities probed via current-induced superconducting phase gradients

We have developed a superconducting phase gradiometer consisting of two parallel DNA-templated nanowires connecting two thin-film leads [1,2,3]. We have ramped the cross current flowing perpendicular to the nanowires, and observed oscillations in the lead-to-lead resistance due to cross-current-induced phase differences. By using this gradiometer we have measured the temperature- and magnetic-field dependence of the superfluid density, and observed an amplification of phase gradients caused by elastic vortex displacements. We examine our data in light of Miller-Bardeen theory of dirty superconductors and a microscale version of Campbell's model of field penetration. \newline [1] Hopkins et al., Science {\bf 308}, 1762 (2005). [2] Pekker et al., Phys. Rev. B {\bf 72}, 104517 (2005). [3] Hopkins et al., Phys. Rev. B Rapid Comm. (2007, in press), accepted for publication.