Retrapping current, self-heating, and hysteretic current-voltage characteristics in ultranarrow superconducting aluminum nanowires

Hysteretic I-V (current-voltage) curves are studied in narrow Al nanowires. The nanowires have a cross section as small as 50 nm². We focus on the retrapping 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 electron and phonon processes. For a short wire 1.5μm in length, electronic thermal conduction is effective; for longer wires 10μm 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 self-heating 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 three dimensions, consistent with the phonon thermal wavelength having exceeded the lateral dimensions at temperatures below ∼1.3 K. Nevertheless, surprisingly the best fit was achieved with a functional form corresponding to three-dimensional phonons, albeit requiring parameters far exceeding known values in the literature.