Fingerprints of spin mediated pairing in cuprates

We demonstrate that the feedback effect from bosonic excitations on fermions, which in the past allowed one to verify the phononic mechanism of a conventional, s-wave superconductivity, may also allow one to experimentally detect the 'fingerprints' of the pairing mechanism in cuprates. We argue that for spin-mediated d-wave superconductivity, the fermionic spectral function, the density of states, the tunneling conductance through an insulating junction, and the optical conductivity are affected by the interaction with collective spin excitations, which below T_c are propagating, magnon-like quasiparticles with gap Δ_s. We show that the interaction with a propagating spin excitation gives rise to singularities at frequencies Δ+Δ_s for the spectral function and the density of states, and at 2Δ+Δ_s for tunneling and optical conductivities, where Δ is the maximum value of the d-wave gap. We further argue that recent optical measurements also allow one to detect subleading singularities at 4Δ and 2Δ+2Δ_s. We consider the experimental detection of these singularities as a strong evidence in favor of the magnetic scenario for superconductivity in cuprates.