This paper proposes a simple local probe to read the complex phase pattern of a topological superconductor. The authors suggest replacing a single superconducting scanning tunneling microscope (STM) tip with a phase‑coherent “fork” made of two tips connected to the same electrode. When placed near a small impurity, this two‑tip setup acts like a tiny interferometer. It converts differences in the superconducting phase at two nearby points into a measurable change in the Josephson current between tip and sample.

Why this matters: the phase of a superconducting order parameter carries crucial information about unconventional and topological superconductors. Standard probes such as photoemission or heat transport tell you about the energy gap and excitations, but not the local phase. Even single‑tip Josephson STM can measure the size of the gap locally, but thermal fluctuations wash out the phase when the tip coupling is weak. The fork‑tip design keeps the two tips locked to the same fluctuating phase, so the relative phase between the two tip positions survives those fluctuations and produces an interference signal that reveals phase differences in the sample.

What the researchers did: they derived how the Josephson current of the fork depends on the two tip positions and the local superconducting order. They show that the interference term in the critical current depends directly on the phase difference of the anomalous Green’s function between the two tip locations. They then computed numerical interference patterns near a single point impurity for different kinds of order parameters. The simulations show clear spatial patterns — for example hyperbolic fringes when the two tips are coherent and characteristic nodal features when the order parameter has nodes — that encode both the magnitude and the angular dependence of the gap and its phase.