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In a superconductor, where electrons move in pairs without resistance, special waves can run along the edges, like ripples along the edge of a carpet. The number of such waves is an important characteristic of the material, but measuring it directly is difficult. Scientists have proposed a clever tool: a movable wall inside the superconductor that separates regions with different "twist" of electron pairs.

When the wall is opened, it becomes a channel for heat. By measuring the amount of heat passing through, you can precisely count how many edge waves run along it. It's like counting people passing through a turnstile by the number of steps. When the wall is closed, it turns into a resonator — a cavity where thermal waves reflect off the walls. If quantum vortices (tiny magnetic knots) are trapped inside, the resonator shifts by half a step. This shift reveals the parity of the number of vortices — whether it's even or odd.

The authors calculated in detail how heat passes through the wall and found a way to distinguish a genuine signal from a false one. A false signal can come from a vortex stuck to the wall from the outside. But by varying temperature, geometry, and monitoring noise, the false vortex gives itself away. Calculations for layers of graphene with a special twist show that loops smaller than a micron at temperatures of thousandths of a kelvin already produce a clear signal. This is a real path to testing exotic superconductors that could become the basis for quantum computers.

Original abstract

as written by the authors arXiv:2608.19343v1

A chiral superconductor carries chiral Majorana modes along its boundary, and the integer that counts them fixes everything that follows, yet that integer has never been measured together with a local parity observable on one object. Proximitized one-dimensional wires read fermion parity rapidly but diagnose bulk topology through a separate protocol. Here we show that a reconfigurable domain wall between regions of opposite Chern number in an intrinsic two-dimensional chiral superconductor performs both functions. Opened to its contacts the wall is a ballistic channel whose quantized thermal conductance counts its Majorana modes; closed, the same wall is a Fabry--P\'erot resonator whose spectrum shifts by half a level spacing when the parity of the enclosed vortices changes, giving a two-level heat conductance. We derive the exact transmission, the elastic heat full counting statistics, and a theorem showing that linear-response heat scattering of a fixed quadratic problem resolves vortex parity but not the fusion channel of well-separated cores. An outside vortex hybridized with the wall is an intrinsic false positive; temperature, geometry and a finite-bias mean--noise test separates it. Rhombohedral-graphene parameters place submicron loops in the resolved regime at millikelvin temperatures, where chiral-domain reconfiguration and noise thermometry are both established.