Vortex viscosity in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ at low temperatures

With a bolometric technique, we have measured, in intense fields, the low-temperature surface resistance of both 90- and 60-K ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals. In the former, the observed vortex viscosity ${\mathrm{\eta }}_{\mathrm{eff}}$=5×${10}^{\mathrm{-}5}$ N s/${\mathrm{m}}^2$ exceeds by 2 orders of magnitude the viscosity in conventional superconductors. This corresponds to a normal-state resistivity of 0.4 μΩ cm, and a quasiparticle lifetime τ∼6 ps. (The corresponding numbers for the 60-K crystal are ${\mathrm{\eta }}_{\mathrm{eff}}$=2.5×${10}^{\mathrm{-}6}$ N s/${\mathrm{m}}^2$ and τ=1.9 ps at 3 K.) These lifetimes place ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ firmly in the superclean regime where the lifetime broadening of core energy levels is much less than the energy spacing. We discuss how a very large Hall angle in this regime affects the analysis of surface resistance.