Determine whether interferometry distinguishes the candidate non-Abelian orders

Determine whether Fabry–Perot and chiral Mach–Zehnder interferometry can distinguish the different non-Abelian topological orders of the 16-fold way proposed for the fractional quantum spin Hall effect, and establish whether these interferometric schemes can at least distinguish Abelian from non-Abelian order.

Background

Approximately half of the candidate composite-fermion states considered in the paper are non-Abelian and contain Majorana sectors characterized by the 16-fold way. The paper discusses noise, thermal conductance, and a two-point-contact transport probe, but does not develop an interferometric analysis.

The authors note that the interpretation of existing interferometry experiments in non-Abelian quantum Hall systems remains difficult. They therefore leave unresolved whether Fabry–Perot and chiral Mach–Zehnder interferometry can distinguish the candidate non-Abelian orders in the fractional spin Hall setting, while identifying canonical Mach–Zehnder interferometry as potentially more powerful but experimentally challenging.

References

It is presently unclear, if the Fabry-Perot and chiral Mach-Zehnder approaches can tell different non-Abelian orders of the 16-fold way from each other. Doubts were raised even about their ability to distinguish Abelian and non-Abelian order. The canonical Mach-Zehnder technique appears more powerful but this comes at a price of fabrication challenges. Besides, the theory is much more involved technically in the Mach-Zehnder case. We thus leave a discussion of interferometry in the fractional spin Hall effect to future work.

— Composite fermions in the $ν=3$ fractional quantum spin Hall effect  (2608.24059 - Liu et al., 25 Aug 2026) in Conclusions, final discussion of interferometry