A Josephson junction is usually a straight line — two superconductors separated by a thin normal region, with the magnetic flux varying continuously across the width. The critical current oscillates with flux in a Fraunhofer pattern: the same sinc function that describes single-slit diffraction. The physics is clean and well-understood. The pattern encodes the junction geometry, and for a rectangular junction, the information it carries is simple: width and critical current density.
Lesser, Park, Ronen, Werkmeister, Kim, and Oreg (arXiv 2601.14364, January 2026) close the junction into a ring. A Corbino geometry: inner superconducting pad, annular normal region, outer superconducting pad. The flux is now quantized — it threads a closed loop, so it takes discrete values — and the superconducting phase must wind by an integer multiple of 2pi around the circumference. The Fraunhofer pattern vanishes.
If the ring is circular, nothing interesting happens. Superconductivity dies as soon as vortices enter, and the critical current stays at zero. The circular geometry distributes the phase gradient uniformly, and the destructive interference is total.
If the ring has corners, everything changes.
A square Corbino junction has phase gradients that concentrate at the four corners — the phase evolves faster there, creating kinks in the spatial profile of the phase difference across the junction. These kinks cause partial cancellation of the supercurrent contributions from different parts of the loop. But at specific flux values — when the number of enclosed vortices is a multiple of four, matching the number of corners — the kinks align constructively, and supercurrent reappears. Superconductivity dies and revives periodically as vortices enter, with the period set by the geometry. A hexagonal junction would revive every six vortices. A triangular one every three.
The reentrant superconductivity is a geometric resonance: the shape of the boundary determines when the phase kinks cooperate instead of canceling.
Now deposit the superconductors on a topological insulator. The junction acquires chiral Majorana modes along its length, modifying the current-phase relation from the standard sin(phi) to include a sin(2phi) component. The doubled angular frequency in the phase relationship halves the periodicity of the resonance. For a square junction, the critical current now revives every two vortices instead of every four. The topological signature is a factor-of-two change in a discrete, countable period — not a subtle shift in a continuous pattern, but a qualitative halving that's hard to miss experimentally.
This is the key practical contribution. In planar junctions, topological signatures are typically small: slight shifts in the positions of Fraunhofer nodes, minor asymmetries in the interference pattern. Detecting them requires precision measurements and careful modeling. In a polygonal Corbino junction, the question reduces to counting: does the supercurrent revive every N vortices or every N/2? The geometry amplifies the topological signature from a quantitative correction into a qualitative change.
The corner does the work. Without corners, the Corbino junction is featureless — superconductivity dies and stays dead. With corners, it becomes a diagnostic instrument whose readout is a discrete period that directly encodes whether the junction hosts topological modes. The same physical effect — phase kinks from a non-circular boundary — that creates the reentrant superconductivity also creates the sensitivity to topology. The geometry that makes the measurement possible is the same geometry that makes the measurement sharp.