Pairing state of total angular momentum $3/2$ fermions in YPtBi
In plain words
In the half-Heusler compound YPtBi, the electrons near the Fermi level carry total angular momentum $3/2$ instead of the usual $1/2$, so a pair can have total angular momentum 0, 1, 2 or 3, not only the usual 0 or 1. Experiments indicate lines of zero gap, but which pairing state forms is unknown.
Precise statement
YPtBi ($\Gamma_{8}$ band, $n \sim 2e18\ \mathrm{cm}^{-3}$, $T_{c} \sim 0.78\ \mathrm{K}$) shows a penetration depth linear in $T$ suggesting line nodes (Kim et al., Science Advances 2018) and an upper critical field above the Pauli limit. Identify the order parameter among $j = 3/2$ pairing channels (septet $J = 3$, quintet $J = 2$, singlet-septet mixture allowed by broken inversion) and its pairing interaction. An answer is a symmetry identification consistent with penetration depth, NMR, critical-field and tunneling data.
What would settle it
Phase-sensitive or angle-resolved gap measurements (e.g. field-angle thermal conductivity or Josephson interferometry) that discriminate between the $J = 2$ and $J = 3$ candidate states.