  The voltage-carrying state of superconducting NbTiN nanowires, used for
single-photon detectors, is analyzed. Upon lowering the current, the wire
returns to the superconducting state in a steplike pattern, which differs from
sample to sample. Elimination of geometrical inhomogeneities, such as sharp
corners, does not remove these steplike features. They appear to be intrinsic
to the material. Since the material is strongly disordered, electronic
inhomogeneities are considered as a possible cause. A thermal model, taking
into account random variations of the electronic properties along the wire, is
used as an interpretative framework.
