Nonlocal transport in superconducting oxide nanostructures*

We report nonlocal transport signatures in the superconducting state of nanostructures formed\footnote{J.P. Veazey, \textit{et al.}, arXiv:1210.3606 (2012).} at the LaAlO$_3$/SrTiO$_3$ interface using conductive AFM lithography. Nonlocal resistances (nonlocal voltage divided by current) are as large as 200 $\Omega$ when 2-10 $\mu$m separate the current-carrying segments from the voltage-sensing leads. The nonlocal resistance reverses sign at the local critical current of the superconducting state. Features observed in the nonlocal \textit{V-I} curves evolve with back gate voltage and magnetic field, and are correlated with the local four-terminal \textit{V-I} curves. We discuss how nonlocal and local transport effects in LaAlO$_3$/SrTiO$_3$ nanostructures may result from the electronic phase separation and superconducting inhomogeneity reported by others in planar structures\footnote{Ariando, \textit{et al.}, \textit{Nature Comm.} \textbf{2}, 188 (2011); J.A. Bert, \textit{et al.}, \textit{Nature Phys.} \textbf{7}, 767 (2011).}.