Evidence for precursor superconducting pairing above T_c in underdoped cuprates from an analysis of the in-plane infrared response

We performed calculations of the in-plane infrared response of underdoped cuprate superconductors to clarify the origin of a characteristic dip feature which occurs in the published experimental spectra of the real part of the in-plane conductivity below an onset temperature $T^{ons}$ considerably higher than $T_c$. We provide several arguments, based on a detailed comparison of our results with the published experimental data, confirming that the dip feature and the related features of the memory function $M\left(\omega \right)=M_1\left(\omega \right)+i{M}_2\left(\omega \right)$ (a peak in M₁ and a kink in M₂) are due to superconducting pairing correlations that develop below $T^{ons}$. In particular, we show that (i) the dip feature, the peak and the kink of the low-temperature experimental data can be almost quantitatively reproduced by calculations based on a model of a d-wave superconductor. The formation of the dip feature in the experimental data below $T^{ons}$ is shown to be analogous to the one occurring in the model spetra below $T_c$. (ii) Calculations based on simple models, for which the dip in the temperature range from $T_c$ to $T^{ons}$ is unrelated to superconducting pairing, predict a shift of the onset of the dip at the high-energy side upon entering the superconducting state, that is not observed in the experimental data; (iii) the conductivity data in conjunction with the recent photoemission data (Reber et al 2012 Nat. Phys. 8 606, Reber et al 2013 Phys. Rev. B 87 060506) imply the persistence of the coherence factor characteristic of superconducting pairing correlations in a range of temperatures above $T_c$. (paper)