In-plane electronic confinement in superconducting LaAlO$_3$/SrTiO$_3$ nanostructures

We describe the transport properties of mesoscopic devices based on the two dimensional electron gas (2DEG) present at the LaAlO$_3$/SrTiO$_3$ interface. Bridges with lateral dimensions down to 500~nm were realized using electron beam lithography. Their detailed characterization shows that processing and confinement do not alter the transport parameters of the 2DEG. The devices exhibit superconducting behavior tunable by electric field effect. In the normal state, we measured universal conductance fluctuations, signature of phase-coherent transport in small structures. The achievement of reliable lateral confinement of the 2DEG opens the way to the realization of quantum electronic devices at the LaAlO$_3$/SrTiO$_3$ interface.