Anisotropic magnetoresistance of a one-dimensional superconducting niobium strip

We investigated confinement effects on the resistive anisotropy of a superconducting niobium strip with a rectangular cross-section. When the strip's transverse dimensions are comparable to the superconducting coherence length, we find the angle dependent magentoresistances at a fixed temperature can be scaled as R($\theta $, H) = R(H /H$_{c\theta })$ where H$_{c\theta }$ = H$_{c0}$ (cos$^{2}\theta +\gamma ^{-2}$sin$^{2}\theta )^{-1/2}$ is the angular dependent critical field, $\gamma $ = w/d is the width to thickness ratio of the strip, and H$_{c0}$ is the out-plane critical field at $\theta $ = 0\r{ }. Our results can be understood in terms of the anisotropic diamagnetic energy of a one-dimensional superconductor in a magnetic field.