Low energy theory of a single vortex and electronic quasiparticles in a   d-wave superconductor
  We highlight the properties of a simple model (contained in our recent work) of the quantum dynamics of a single point vortex interacting with the nodal fermionic quasiparticles of a d-wave superconductor. We describe the renormalization of the vortex motion by the quasiparticles: at T=0, the quasiparticles renormalize the vortex mass and introduce only a weak sub-Ohmic damping. Ohmic (or `Bardeen-Stephen' damping) appears at T>0, with the damping co-efficient vanishing ~ T^2 with a universal prefactor. Conversely, quantum fluctuations of the vortex renormalize the quasiparticle spectrum. A point vortex oscillating in a harmonic pinning potential has no zero-bias peak in the electronic local density of states (LDOS), but has small satellite features at an energy determined by the pinning potential. These are proposed as the origin of sub-gap LDOS peaks observed in scanning tunneling microscopic studies of the LDOS near a vortex. 
Predrag Nikolic and Subir Sachdev