Description
$SrTiO_3$ is a superconducting semiconductor whose pairing
mechanism has remained mysterious for more than half a
century. The development of $SrTiO_3$-based
heterostructures and nanostructures has enabled systematic
investigation of the role of dimensionality on superconducting
behavior. Here, we examine superconductivity in a family of
$LaAlO_3/SrTiO_3$ channels whose widths systematically
traverse the 1D-2D transition. The superconducting critical
current of $LaAlO_3/SrTiO_3$ is found to be independent of
width ranging from 10-1000 nm; the narrower channels
exhibit densities that are at least an order of magnitude
larger than for macroscopic 2D $LaAlO_3/SrTiO_3$
interfaces. Increasing the number of 1D channels results in a
marked increase in critical current and suppression of
background resistance. Resistive anomalies outside of the
superconducting regime are observed for the narrow
channels, and are attributed to a state in which electrons are
paired but not superconducting. These results strongly
indicate that electron pairing?and superconductivity?exist
only along the boundaries of these channels and are absent
within the interior region of the channels. These experiments
provide new physical constraints on possible pairing
mechanisms for $SrTiO_3$-based systems.