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. Th
eir 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.
We report transport measurements through graphene on SrTiO3 substrates as a function of magnetic field B, carrier density n, and temperature T. The large dielectric constant of SrTiO3 screens very effectively long-range electron-electron interactions
and potential fluctuations, making Dirac electrons in graphene virtually non-interacting. The absence of interactions results in a unexpected behavior of the longitudinal resistance in the N=0 Landau level, and in a large suppression of the transport gap in nano-ribbons. The bulk transport properties of graphene at B=0T, on the contrary, are completely unaffected by the substrate dielectric constant.
