Do nematic quantum critical fluctuations enhance $T_c$
In plain words
Near the point where nematic order disappears at zero temperature its fluctuations are strongest, and they might help electrons pair; data in different compounds disagree.
Precise statement
In FeSe1-xSx the nematic transition vanishes near $x \sim 0.17$ without a $T_{c}$ maximum, while in BaFe2(As1-xPx)2 and Ba(Fe1-xCox)2As2 nematic and magnetic critical points lie near the $T_{c}$ maximum. Determine whether nematic fluctuations contribute measurably to pairing given that coupling to lattice strain cuts off the divergence of the nematic correlation length. An answer is a quantitative estimate of the nematic contribution to the pairing interaction with an experimental test, such as $T_{c}$ versus nematic susceptibility under tuned strain.
What would settle it
Strain-tuned measurements of $T_{c}$ and nematic susceptibility in a single system with magnetic and nematic critical points separated, compared with a model calculation.