High-mobility sketched nanostructures at the Al$_2$O$_3$/SrTiO$_3$ interface

A two dimensional electron gas has recently been demonstrated at the interface between amorphous Al$_2$O$_3$ and TiO$_2$-terminated SrTiO$_3$ by atomic layer deposition (ALO/STO).\footnote{S. W. Lee, \textit{et al.}, Nano Lett. \textbf{12}, 4775 (2012).} Similar to LaAlO$_3$/SrTiO$_3$ heterostructrues, when the ALO thickness exceeds a critical thickness, the interface becomes conducting. By using a conducting atomic force microscope tip to control the metal-insulator transition at nanoscale dimensions, we are able to create nanostructures with exceptionally high mobility. Quasi-two-dimensional written structures exhibit Shubnikov de Haas oscillations and mobilities in excess of 2,000 cm$^2$/Vs. Furthermore, by decreasing the channel width to 10 nm width, the mobility becomes as high as 100,000 cm$^2$/Vs.