Multiple pairing states and temperature-dependent gap anisotropy for superconductivity near a nematic quantum-critical point

Superconductivity in many strongly correlated materials appears in proximity to a density-wave or nematic order and is believed to be mediated by quantum-critical (QC) fluctuations of the corresponding order parameter. We argue that fingerprints of QC pairing can be extracted from the angular dependence of the gap $\Delta (\theta)$. We consider pairing by QC nematic fluctuations and show that there exist multiple pairing instabilities within the same symmetry ($s-$wave in our case), with closely spaced transition temperatures $T_{c,n}$. The corresponding $\Delta_n (\theta)$ change sign $8n$ times along the FS. Only the solution with the highest $T_{c,0} =T_c$ develops, but other gap components are induced below $T_c$ and get resonantly enhanced below $T_{c,n}$. This gives rise to strong variation of the angular dependence of the gap below $T_c$. The effect gets much weaker away from a quantum-critical point.