Quantum Transport in Oxide Nanostructures

We describe low-temperature magnetotransport experiments in nanostructures formed at the LaAlO$_3$/SrTiO$_3$ interface using a conducting 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).} Measurements on a 6-nm wide Hall cross containing $N\approx 250$ electrons (density $n=1.6x10^{12}cm^{-2}$) show evidence for quantized conductance, with notable departures from traditional quantized Hall behavior. A pronounced weak antilocalization feature near $B=0$ is exhibited in both the Hall and magnetoresistance channels, indicating the presence of significant spin-orbit (Rashba) coupling. A 14-nm wide nanowire with lower carrier density (density $n=8.5x10^{11}cm^{-2}$) exhibits magnetoresistance plateaus associated with integer Landau level filling factors $\nu$=2,3,...,9, and the fractional filling factors $\nu$=7/3 and 11/5. The ability to fashion conducting structures with extreme nanoscale dimensions and distinct signatures of quantum transport opens new opportunities for the development of novel quantum devices.