Anomalous Current-Voltage Characteristics of Submicron High-$T_c$ Superconducting Wires

We report anomalous non-linearities in the superconducting current-voltage characteristics of submicron YBa$_2$Cu$_3$O$_{7- \delta}$ wires. Submicron-wide and 100$\mu$m-long samples were fabricated using a chemical-free technique based on selective epitaxial growth. Both current-biased and voltage-biased measurements were made between 4.2 K and $T_c$, using pulsed signals to minimize Joule heating. $S$-shaped non-linearities were observed under voltage-biasing and sharp discontinuities were observed under current-biasing, in striking agreement with phase-slip phenomenology established for low-$T_c$ superconductors in quasi-1D geometries. For our quasi-2D high- $T_c$ wires, these observations indicate the formation of phase- slip lines transverse to the current.