Photoexcited quasiparticle relaxation dynamics are investigated in a $YBa_{ 2}Cu_{ 3}O_{ 7-\delta}$ superconductor as a function of doping $\delta$ and temperature $T$ using ultrafast time-resolved optical spectroscopy. A model calculation is presented which describes the temperature dependence of the photoinduced quasiparticle population $n_{ pe}$, photoinduced transmission $\Delta{ \cal T}/{ \cal T}$ and relaxation time $\tau $ for three different superconducting gaps: (i) a temperature-dependent collective gap such that ${ \bf \Delta}(T)\to 0$ as $T\to T_{ c}$, (ii) a temperature-independent gap, which might arise for the case of a superconductor with pre-formed pairs and (iii) an anisotropic (e.g. d-wave) gap with nodes. Comparison of the theory with data of photoinduced transmission $| \Delta{ \cal T}/{ \cal T} |$, reflection $| Delta{ \cal R}/{ \cal R}|$ and quasiparticle recombination time $\tau$ in $YBa_{ 2}Cu_{ 3}O_{ 7-\delta}$ 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 $YBa_{ 2}Cu_{ 3}O_{ 7-\delta}$ ($0.15<\delta <0.48$). A pure d-wave gap was found to be inconsistent with the data.
Categories: cond-mat.supr-con