We report on the growth and characterization of ultrathin YBa$_2$Cu$_3$O$_{7-delta}$ (YBCO) films on MgO (110) substrates, which exhibit superconducting properties at thicknesses down to 3 nm. YBCO nanowires, with thicknesses down to 10 nm and widths down to 65 nm, have been also successfully fabricated. The nanowires protected by a Au capping layer show superconducting properties close to the as-grown films, and critical current densities, which are only limited by vortex dynamics. The 10 nm thick YBCO nanowires without the Au capping present hysteretic current voltage characteristics, characterized by a voltage switch which drives the nanowires directly from the superconducting to the normal state. Such bistability is associated in NbN nanowires to the presence of localized normal domains within the superconductor. The presence of the voltage switch, in ultrathin nanostructures characterized by high sheet resistance values, though preserving high quality superconducting properties, make our nanowires very attractive devices to engineer single photon detectors.
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