Quasiparticle relaxation dynamics in superconductors with different gap structures: Theory and experiments on ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

Photoexcited quasiparticle relaxation dynamics are investigated in a ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ superconductor as a function of doping δ and temperature $T$ using ultrafast time-resolved optical spectroscopy. A model calculation is presented that describes the temperature dependence of the photoinduced quasiparticle population $n_{\mathrm{pe}},$ photoinduced transmission $\Delta \mathcal{T}/\mathcal{T},$ and relaxation time τ for three different superconducting gaps: (i) a temperature-dependent collective gap such that $\mathit{\Delta }\mathrm{}\left(T\right)\mathrm{}\to 0$ as $\overrightarrow{T}{T}_c,$ (ii) a temperature-independent gap, which might arise for the case of a superconductor with preformed pairs, and (iii) an anisotropic (e.g., $d$-wave) gap with nodes. Comparison of the theory with data of photoinduced transmission $|\Delta \mathcal{T}/\mathcal{T}|,$ reflection $|\Delta \mathcal{R}/\mathcal{R}|,$ and quasiparticle recombination time τ in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ over a very wide range of doping $(0.1<\delta <0.48)$ is found to give good quantitative agreement with a temperature-dependent BCS-like isotropic gap near optimum doping $(\delta <0.1)$ and a temperature-independent isotropic gap in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}(0.15<\delta <0.48).\mathrm{}$ A pure $d$-wave gap was found to be inconsistent with the data.