Determine the Chern number of the Fu–Kane vortex lattice

Determine the Chern number of the Majorana bands generated by intervortex hybridization in a proximity-induced Fu–Kane superconducting vortex lattice as a function of magnetic field and microscopic parameters, thereby identifying the regime in which the boundary central charge remains $1$.

Background

Intervortex tunneling can hybridize Fu–Kane Majorana zero modes into dispersive bands. If those bands have nonzero Chern number, they contribute an additional chiral central charge and change the nominal thermal-conductance value of the boundary.

The paper assumes the trivial regime with zero Majorana-band Chern number for its parameter-free result, but notes that the relevant calculation has not been carried out explicitly for the proximity-induced Fu–Kane system. Establishing the Chern-number phase diagram is therefore necessary to determine the experimentally accessible regime.

References

For the proximity-induced Fu--Kane SC the analysis has not been carried out explicitly, but $\mathcal{C}_M \in {0,\pm 1}$ is the natural expectation by the same symmetry-class analysis.

— Topological and kinetic origins of fractional thermal conductance at the topological insulator--superconductor interface  (2610.10011 - Jacobs et al., 7 Oct 2026) in Section 4.1, “Topological realization: the anomaly of the TI–SC boundary”; Section 5, final paragraph of secondary directions