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

Abstract

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, ωm) and show that its angular dependence strongly varies below Tc. 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 Tc,n. Taken alone, each instability would produce a gap Δ (θ, ωm) that changes sign 8 n times along the Fermi surface. We show that the equilibrium gap Δ (θ, ωm) is a superposition of multiple components that are nonlinearly induced below the actual Tc= Tc , 0, and get resonantly enhanced at T=Tc,n