Effective action for vortex dynamics in clean d-wave superconductors

We describe the influence of the gapless, nodal, fermionic quasiparticles of a two-dimensional d-wave superconductor on the motion of vortices. A continuum, functional formalism is used to obtain the effective vortex action, after the fermions have been integrated out. At zero temperature (T), the leading terms in the vortex action retain their original form, with only an infrared finite renormalization of the vortex effective mass from the fermions. A universal "sub-Ohmic" damping of the vortex motion is also found. At T > 0, we find a Bardeen-Stephen viscous drag term, with a universal coefficient which vanishes as similar to T-2. We present a simple scaling interpretation of our results, in which quantum-critical Dirac fermions respond to a moving point singularity. Our results appear to differ from those of the semiclassical theory, which obtains more singular corrections to a vortex mass appearing in transport equations.