Transport regimes of a split gate superconducting quantum point contact in the two-dimensional LaAlO₃/SrTiO₃ superfluid

One of the hallmark experiments of quantum transport is the observation of the quantized resistance in a point contact in GaAs/AlGaAs heterostructures. Being formed with split gate technology, these structures represent in an ideal manner equilibrium reservoirs which are connected only through a few electron mode channel. It has been a long standing goal to achieve similar experimental conditions also in superconductors. Here we demonstrate the formation of a superconducting quantum point contact (SQPC) with split gate technology in a two-dimensional superconductor, utilizing the unique gate tunability of the superfluid at the LaAlO₃/SrTiO₃ interface. When the constriction is tuned through the action of metallic split gates we identify three regimes of transport: First, SQPC for which the supercurrent is carried only by a few quantum transport channels. Second, superconducting island strongly coupled to the equilibrium reservoirs. Third, charge island with a discrete spectrum weakly coupled to the reservoirs.