Quasiparticle energy relaxation in the cuprate superconductors

Abstract

At high flux-flow velocities in the mixed state of a type-II superconductor the nonequilibrium distribution of the quasiparticles is shifted to higher energies. As shown theoretically by Larkin and Ovchinnikov, a distinct signature of this nonequilibrium effect is an electronic instability, resulting in a sharp kink in the current-voltage characteristic at a critical vortex velocity ${v}_{\ensuremath{\varphi}}^{*}.$ From measurements of ${v}_{\ensuremath{\varphi}}^{*}$ the quasiparticle-energy relaxation rate ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}^{\ensuremath{-}1}$ can be found. We have measured this instability point for epitaxial $c$ axis oriented films of ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_{4\ensuremath{-}x}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}.$ In both cuprates the observed temperature dependence of ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}^{\ensuremath{-}1}$ could be well fitted with the function ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}^{\ensuremath{-}1}=a\mathrm{exp}[\ensuremath{-}2\ensuremath{\Delta}{(T)/k}_{B}T],$ suggesting that the electron-electron recombination process, perhaps in combination with the emission of another excitation, is crucial. As an example of a low-${T}_{c}$ superconductor we have also studied amorphous ${\mathrm{Mo}}_{3}\mathrm{Si}$ films and found that ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}^{\ensuremath{-}1}$ can be fitted by a function similar to that we have used for the cuprates, again indicating the importance of the electron-electron interaction.