Interpretation of in-plane infrared response of high-Tccuprate superconductors involving spin fluctuations using quasiparticle spectral functions

The in-plane infrared response of the high-${T}_{c}$ cuprate superconductors was studied using the spin-fermion model, where charged quasiparticles of the copper-oxygen planes are coupled to spin fluctuations. First, we analyzed structures of the superconducting-state conductivity reflecting the coupling of the quasiparticles to the resonance mode observed by neutron scattering. The conductivity $\ensuremath{\sigma}$ computed with the input spin susceptibility in the simple form of the mode exhibits two prominent features: an onset of the real part of $\ensuremath{\sigma}$ starting around the frequency ${\ensuremath{\omega}}_{0}$ of the mode and a maximum of a related function $W(\ensuremath{\omega})$, roughly proportional to the second derivative of the scattering rate $[1∕\ensuremath{\tau}](\ensuremath{\omega})$, centered approximately at $\ensuremath{\omega}={\ensuremath{\omega}}_{0}+{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$, where ${\ensuremath{\Delta}}_{0}$ is the maximum value of the superconducting gap. The two structures are well-known from earlier studies. Their physical meaning, however, has not been sufficiently elucidated thus far. Our analysis involving quasiparticle spectral functions provides a clear interpretation. Second, we explored the role played by the spin-fluctuation continuum, whose spectral weight is known to be much larger than the one of the mode. We have shown that the experimental spectra of $1∕\ensuremath{\tau}$ can be approximately reproduced by augmenting the resonant-mode component of the spin susceptibility by a suitable continuum component with a considerably higher spectral weight and with a characteristic width of several hundreds meV. The computed spectra of $1∕\ensuremath{\tau}$ display a new structure in the midinfrared which is related to the finite width of the occupied part of the conduction band. Third, we investigated the temperature dependence (TD) of $\ensuremath{\sigma}$ assuming that the normal state spin susceptibility consists of an overdamped low energy mode and the continuum component. The differences between the experimental normal-state spectra and those of the superconducting state, including some interesting effects at higher frequencies, are reasonably well-reproduced. Motivated by recent experimental (ellipsometric) works by Molegraaf and co-workers [H. J. A. Molegraaf et al., Science 295, 2239 (2002)] and Boris and co-workers [A. V. Boris et al., Science 304, 708 (2004)], we further studied the TDs of the effective kinetic energy (KE) and of the intraband spectral weight ${I}_{O}$. Calculations for the trivial case of noninteracting quasiparticles in the normal state and a BCS-like superconducting state reveal a strong sensitivity of the TD of ${I}_{O}$ to details of the dispersion relation. The TDs of KE and ${I}_{O}$ in the interacting case, for the set of the values of the input parameters used throughout this work, are similar to those of the trivial case. The physics beyond the changes occurring when going from the normal to the superconducting state, however, is shown to be more complex, involving, besides the formation of the gap, also a feedback effect of the spin fluctuations on the quasiparticles and a significant shift of the chemical potential.