##
Effective Action for Vortex Dynamics in Clean d-wave Superconductors

Predrag Nikolic **Harvard**
__Abstract:__

We describe influence of gapless nodal quasiparticles on vortex dynamics in clean two-dimensional d-wave
superconductors. At zero temperature, the guasiparticles give rise to a finite renormalization of vortex mass,
as well as a universal sub-Ohmic damping of vortex motion. Slow vortex motion is dissipated only at finite
temperatures, or when some perturbation, such as disorder, creates a finite quasiparticle density of states at
the gap nodes. These results are obtained by a non-perturbative derivation of the effective vortex action, where
the quasiparticles are integrated out exactly in a continuum functional formalism. An uncontrolled perturbative
analysis reaches the same conclusions, and all findings are reflected in a simple scaling argument where the
gapless Dirac quasiparticles are regarded as a quantum-critical system. Our results appear to differ from those
of the semiclassical theory, which obtains singular corrections to a vortex mass appearing in transport
equations.