Microwave measurements of vortex dynamics in the heavy fermion superconductor CeCoIn$_5$

Magnetic fields penetrate superconductors as a lattice of quantized tubes of magnetic flux, or ``vortices.'' A transport current, passed through such a superconductor, exerts a transverse component of force on the vortex lattice. Subsequent motion of the vortices results in dissipation. The frictional force experienced by a moving flux line is parameterized by a \emph{vortex viscosity}, and arises from induced electric fields coupling to charge excitations in the vicinity of the vortex core. We present vortex viscosity data on the heavy fermion superconductor CeCoIn$_5$, obtained using sensitive new microwave apparatus that operates at temperatures down to 0.07~mK and magnetic fields up to 9~T. The data we obtain is surprising, and indicates a breakdown of Bardeen--Stephen theory in this material; instead of arising from normal currents in the vortex cores, the frictional forces on the vortices appear to be caused by interactions with $d$-wave quasiparticles \emph{outside} the cores. This is evident in two ways: from the temperature dependence of the viscosity, which mirrors that of the $d$-wave quasiparticle conductivity; and from the observation of a new type of Volovik effect, in which the vortex viscosity has a $\sqrt{B}$ dependence on magnetic field.