Quasiparticle relaxation dynamics in superconductors with different gap structures: Theory and experiments onYBa2Cu3O7−δ

Abstract

Photoexcited quasiparticle relaxation dynamics are investigated in a ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ superconductor as a function of doping \ensuremath{\delta} 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 $\ensuremath{\Delta}\mathcal{T}/\mathcal{T},$ and relaxation time \ensuremath{\tau} for three different superconducting gaps: (i) a temperature-dependent collective gap such that $\mathit{\ensuremath{\Delta}}(T)\ensuremath{\rightarrow}0$ as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c},$ (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 $|\ensuremath{\Delta}\mathcal{T}/\mathcal{T}|,$ reflection $|\ensuremath{\Delta}\mathcal{R}/\mathcal{R}|,$ and quasiparticle recombination time \ensuremath{\tau} in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ over a very wide range of doping $(0.1<\ensuremath{\delta}<0.48)$ is found to give good quantitative agreement with a temperature-dependent BCS-like isotropic gap near optimum doping $(\ensuremath{\delta}<0.1)$ and a temperature-independent isotropic gap in underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}(0.15<\ensuremath{\delta}<0.48).$ A pure $d$-wave gap was found to be inconsistent with the data.