Free flux flow resistivity in a strongly overdoped high-$T_c$ cuprate: The purely viscous motion of the vortices in a semiclassical d-wave superconductor

We report the free flux flow (FFF) resistivity associated with a purely viscous motion of the vortices in a moderately clean d-wave superconductor Bi:2201 in the strongly overdoped regime ${(T}_c=16\mathrm{}\hspace{0.5em}\mathrm{K})$ for a wide range of the magnetic field in the vortex state. The FFF resistivity is obtained by measuring the microwave surface impedance at different microwave frequencies. It is found that the FFF resistivity is remarkably different from that of conventional s-wave superconductors. At low fields $(H<\mathrm{}{0.2H}_{c2\mathrm{}})$ the FFF resistivity increases linearly with H with a coefficient which is far larger than that found in conventional s-wave superconductors. At higher fields, the FFF resistivity increases in proportion to $\sqrt{H}$ up to $H_{c2\mathrm{}}.$ Based on these results, the energy dissipation mechanism associated with the viscous vortex motion in “semiclassical” d-wave superconductors with gap nodes is discussed. Two possible scenarios are put forth for these field dependences: the enhancement of the quasiparticle relaxation rate and the reduction of the number of the quasiparticles participating the energy dissipation in d-wave vortex state.