Majorana modes in half-quantum vortices of polar-distorted 3He
In plain words
In helium-3 inside nematic aerogel (a porous solid of aligned strands), vortices carrying half of the usual circulation were observed in 2016. Theory says that in some of these phases each such vortex core holds a Majorana zero mode, which has not been detected.
Precise statement
Half-quantum vortices were observed by NMR in the polar phase of 3He in nafen (Autti et al. 2016) and survive into the polar-distorted A phase (Makinen et al. 2019). Determine whether their cores in the polar-distorted A phase bind Majorana zero modes and detect them, e.g. through core-bound-state contributions to NMR relaxation, thermal transport or vortex dynamics. An answer is yes or no with core-state spectroscopy.
What would settle it
A measured core-state signal (relaxation rate or heat transport) scaling with half-quantum vortex density and matching the predicted zero-mode spectrum.
Status in the literature
Half-quantum vortex existence was settled in 2016 to 2019; the zero-mode question remains open.