Electric-field lithography of LaAlO$_{3}$/SrTiO$_{3}$ quasi-two-dimensional electron gas*

Recent reports$^{2,3}$ have indicated that the existence of polar discontinuities at the interface between LaAlO$_{3}$ and SrTiO$_{3}$ is unstable to the formation of a quasi-two-dimensional electron gas. Below a critical thickness electrons can still accumulate at the interface under the influence of an applied electric field$^{3}$. We use a biased conducting atomic force microscope (AFM) probe to create conducting nanowires at the LaAlO$_{3}$/SrTiO$_{3}$ interface without physical alteration of the interface. The conducting regions written by AFM probe can be written and erased repeatedly. This form of quasi-two-dimensional lithography demonstrates the utility of the LaAlO$_{3}$/SrTiO$_{3}$ interface as a rewritable medium, with the potential for creating passive as well as active circuits such as field-effect transistors. ( $^{2}$ A. Ohtomo and H. Y. Hwang, Nature \textbf{427}, 423 (2004). $^{3}$ S. Thiel, G. Hammerl, A. Schmehl, C. W. Schneider, and J. Mannhart, Science \textbf{313}, 1942 (2006).)