Nanoscale rectification at the LaAlO$_3$/SrTiO$_3$ interface

We report nanoscale electrical rectification in nanowires formed at the interface between LaAlO$_{3}$ and SrTiO$_{3}$. Using an AFM writing technique\footnote{C. Cen, S. Thiel, K. E. Andersen, C. S. Hellberg, J. Mannhart, and J. Levy, Nature Materials \textbf{7}, 2136 (2008).}$^,$\footnote{C. Cen, S. Thiel, J. Mannhart, and J. Levy, Science \textbf{323}, 1026 (2009).} it is possible to create conducting nanoregions with a precision that approaches the atomic scale. Here we demonstrate how controlled asymmetries in the in-plane potential profile along a nanowire lead to controlled electrical rectification, similar to that observed in Schottky diodes.