Compute the vortex Fano factor and noise-scaling exponent

Compute the material-dependent Fano factor for tunneling of fractionally charged $e/4$ vortices at the topological-insulator–superconductor interface, including correlations in the Abrikosov vortex array, and determine the resulting magnetic-field scaling exponent of the topological shot-noise signal.

Background

The proposed shot-noise diagnostic distinguishes topological vortex transport from kinetic IQH equilibration through their different magnetic-field dependences. Its topological contribution contains an unknown Fano factor and assumes a provisional square-root dependence on the number of vortices.

Because vortices form a positionally ordered and interacting Abrikosov array rather than an independent Poissonian gas, correlations may modify the assumed scaling. The required calculation must therefore account for both the fractional vortex charge and the Majorana-sector statistics of the composite excitation.

References

The factor $\mathcal{F}_v$ for $e/4$ vortex tunneling in eq:S_top is the sole material-dependent unknown in the shot-noise diagnostic and has not been computed.

— Topological and kinetic origins of fractional thermal conductance at the topological insulator--superconductor interface  (2610.10011 - Jacobs et al., 7 Oct 2026) in Section 5, “Open problems and future directions,” third problem; see also Section 4.2