  We theoretically study a strongly disordered superconducting layer heated by
near-field microwave radiation from a nanometric metallic tip. The microwaves
heat up the quasiparticles, which cool by phonon emission and conduction away
from the heated area. Due to a bistability with two stable states of the
electron temperature under the tip, the heating can be tuned to induce a
submicrometer-sized normal region bounded by a sharp domain wall between high-
and low-temperature states. We propose this as a local probe to access
different physics from existing methods, for example, to map out inhomogeneous
superfluid flow in the layer. The bistability-induced domain wall can
significantly improve its spatial resolution.
