Nonequilibrium effects in superconducting necks of nanoscopic dimensions

We have fabricated superconducting connecting necks of Pb with a scanning tunneling microscope (STM) and studied their properties under magnetic fields near the transition to the resistive state. A striking phenomenology is found with two well defined conduction regimes as a function of the magnetic field. We discuss the possible origin of this behavior in terms of the interplay between the field dependence of the quasiparticle charge imbalance length ${\mathrm{\Lambda }}_{Q\ast }$ and the length of the neck which is superconducting under field.