Multiple intertwined pairing states and temperature-sensitive gap anisotropy for superconductivity at a nematic quantum-critical point

The proximity of many strongly correlated superconductors to density-wave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantum-critical (QC) fluctuations of the corresponding order parameter. Here we study anisotropic s-wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the non-linear gap equation for the pairing gap Δ (θ, ω_m) and show that its angular dependence strongly varies below T_c. We show that this variation is a signature of QC pairing and comes about because there are multiple s-wave pairing instabilities with closely spaced transition temperatures T_{c , n}. Taken alone, each instability would produce a gap Δ (θ, ω_m) that changes sign 8 n times along the Fermi surface. We show that the equilibrium gap Δ (θ, ω_m) is a superposition of multiple components that are nonlinearly induced below the actual T_c= T_{c , 0}, and get resonantly enhanced at T=Tc,n<Tc. This gives rise to strong temperature variation of the angular dependence of Δ (θ, ω_m). This variation progressively disappears away from a QC point.