Title: Superconductivity and Frozen Electronic States at the (111) LaAlO$_3$/SrTiO$_3$ Interface,
Abstract: In spite of Anderson's theorem, disorder is known to affect superconductivity
in conventional s-wave superconductors. In most superconductors, the degree of
disorder is fixed during sample preparation. Here we report measurements of the
superconducting properties of the two-dimensional gas that forms at the
interface between LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) in the (111) crystal
orientation, a system that permits \emph{in situ} tuning of carrier density and
disorder by means of a back gate voltage $V_g$. Like the (001) oriented LAO/STO
interface, superconductivity at the (111) LAO/STO interface can be tuned by
$V_g$. In contrast to the (001) interface, superconductivity in these (111)
samples is anisotropic, being different along different interface crystal
directions, consistent with the strong anisotropy already observed other
transport properties at the (111) LAO/STO interface. In addition, we find that
the (111) interface samples "remember" the backgate voltage $V_F$ at which they
are cooled at temperatures near the superconducting transition temperature
$T_c$, even if $V_g$ is subsequently changed at lower temperatures. The low
energy scale and other characteristics of this memory effect ($<1$ K)
distinguish it from charge-trapping effects previously observed in (001)
interface samples.