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

Abstract

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 $$\Delta (\theta ,{\omega }_{m})$$ Δ ( θ , ω m ) and show that its angular dependence strongly varies below $${T}_{{\rm{c}}}$$ 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 $${T}_{{\rm{c}},n}$$ T c , n . Taken alone, each instability would produce a gap $$\Delta (\theta ,{\omega }_{m})$$ Δ ( θ , ω m ) that changes sign $$8n$$ 8 n times along the Fermi surface. We show that the equilibrium gap $$\Delta (\theta ,{\omega }_{m})$$ Δ ( θ , ω m ) is a superposition of multiple components that are nonlinearly induced below the actual $${T}_{{\rm{c}}}={T}_{{\rm{c}},0}$$ T c = T c , 0 , and get resonantly enhanced at $$T={T}_{{\rm{c}},n}\ <\ {T}_{{\rm{c}}}$$ T = T c , n < T c . This gives rise to strong temperature variation of the angular dependence of $$\Delta (\theta ,{\omega }_{m})$$ Δ ( θ , ω m ) . This variation progressively disappears away from a QC point.