Self-calibrating thermal interferometry of vortex parity in a two-dimensional chiral superconductor

Certifying topological superconductivity requires measuring both the bulk invariant and a local fermion-parity observable on the same physical system, a combination that has remained experimentally elusive in conventional semiconductor-superconductor heterostructures. This paper investigates whether a single, reconfigurable domain wall in an intrinsic two-dimensional chiral superconductor can simultaneously perform both tasks. The author approaches this by analyzing a closed domain wall separating regions of opposite Chern number, coupled to floating thermal reservoirs via point contacts.

The proposed device operates in two distinct modes on the same physical object. When the point contacts are open, the domain wall functions as a ballistic channel whose quantized thermal conductance directly counts its Majorana modes, serving as a self-calibrating measurement of the bulk invariant. When the contacts are closed, the same wall forms a Fabry-Pérot resonator for the chiral Majorana modes. The boundary conditions of the Majorana field are determined by the parity of the enclosed Abrikosov vortices: even vortex parity yields Neveu-Schwarz boundary conditions, while odd parity yields the Ramond sector with a zero-energy mode. This parity-dependent shift of the resonance comb by half a level spacing translates into a two-level thermal conductance that can be read out using noise thermometry.

Using a minimal single-branch contact model and a real orthogonal scattering matrix, the author derives the exact transmission probability and elastic heat full counting statistics for the loop. Because chiral Majorana modes carry heat rather than charge, thermal transport circumvents the environmental charge noise and Aharonov-Bohm phase sensitivities that complicate electrical interferometry. The thermal conductance calculation reveals that while transparent contacts recover the universal quantized domain-wall plateau, finite transparency converts the spectral shifts into distinguishable heat transmission peaks. The author also establishes that linear-response heat scattering resolves vortex parity but cannot distinguish the individual fusion channels of well-separated non-Abelian cores.