Single-Mode Cooper Pair Channel in LaAlO$_3$/SrTiO$_3$ Nanowires

The conducting LaAlO$_{3}$/SrTiO$_{3}$ interface becomes superconducting\footnote{N. Reyren, \textit{et al.}, Science \textbf{317}, 1196-9 (2007).} below a critical temperature T$_{c}\sim$100-400~mK. Here, we investigate the transport characteristics of LaAlO$_{3}$/SrTiO$_{3}$ structures formed from $\sim$10 nm-wide nanowire segments produced by a conductive atomic force microscope lithography technique\footnote{C. Cen, S. Thiel, K. E. Andersen, C. S. Hellberg, J. Mannhart, and J. Levy, Nature Materials \textbf{7}, 2136 (2008).}. Above T$_{c}\sim$200~mK we find a characteristic four-terminal conductance $G\sim e^{2}/h$ that is independent of the channel length. Below T$_{c}$ we find that the conductance increases to $G\sim 4e^{2}/h$. This increase is attributed to the formation of Cooper pairs that propagate in a single mode. We also discuss the interactions between Cooper pairs and spin-polarized transport in these structures. This work is supported by AFOSR (FA9550-10-1-0524).