  The oxide heterostructure LaAlO3/SrTiO3 supports a two-dimensional electron
liquid with a variety of competing phases including magnetism,
superconductivity and weak antilocalization due to Rashba spin-orbit coupling.
Further confinement of this 2D electron liquid to the quasi-one-dimensional
regime can provide insight into the underlying physics of this system and
reveal new behavior. Here we describe magnetotransport experiments on narrow
LaAlO3/SrTiO3 structures created by a conductive atomic force microscope
lithography technique. Four-terminal local transport measurements on
~10-nm-wide Hall bar structures yield longitudinal resistances that are
comparable to the resistance quantum h/e2 and independent of the channel
length. Large nonlocal resistances (as large as 10^4 ohms) are observed in some
but not all structures with separations between current and voltage that are
large compared to the 2D mean-free path. The nonlocal transport is strongly
suppressed by the onset of superconductivity below ~200 mK. The origin of these
anomalous transport signatures is not understood, but may arise from coherent
transport defined by strong spin-orbit coupling and/or magnetic interactions.
