Retrapping Current, Self-Heating, and Hysteretic Current-Voltage Curves in Ultra-Narrow Superconducting Aluminum Nanowires

Hysteretic I-V (current-voltage) is studied in narrow Al nanowires. The nanowires have a cross section as small as 50 nm^2. We focus on the retapping current in a down-sweep of the current, at which a nanowire re-enters the superconducting state from a normal state. The retrapping current is found to be significantly smaller than the switching current at which the nanowire switches into the normal state from a superconducting state during a current up-sweep. For wires of different lengths, we analyze the heat removal due to various processes, including electronic and phonon processes. For a short wires 1.5 um in length, electronic thermal conduction is effective; for longer wires 10um in length, phonon conduction becomes important. We demonstrate that the measured retrapping current as a function of temperature can be quantitatively accounted for by the selfheating occurring in the normal portions of the nanowires to better than 20 % accuracy. For the phonon processes, the extracted thermal conduction parameters support the notion of a reduced phase-space below 3-dimensions, consistent with the phonon thermal wavelength having exceeded the lateral dimensions at temperatures below ~ 1.3K. Nevertheless, surprisingly the best fit was achieved with a functional form corresponding to 3-dimensional phonons, albeit requiring parameters far exceeding known values in the literature.