Spin-orbit engineering of LaAlO$_3$/SrTiO$_3$ nanowires

LaAlO$_3$/SrTiO$_3$ heterostructures possess a tunable spin-orbit coupling that strongly influences other properties such as magnetism and superconductivity. Low-temperature transport experiments with nanowires created by conductive AFM show a sizeable non-zero resistance in the superconducting state. Here we present low-temperature magnetotransport of nanowires with 1D corrugations (e.g., triangular and rectangular lattices). We find that these ``zig-zag'' nanostructures possess a robust, fully superconducting state as compared to conventional ``straight'' nanowires. The most likely explanation relates to an effective spin-orbit interaction in which the effective magnetic fields of segments within the zig-zag ``unit cell'' cancel. We discuss implications for engineering spin-orbit couplings in superconducting nanostructures capable of supporting Majorana zero modes.