Model for nodal quasiparticle scattering in a disordered vortex lattice

Abstract

Recent scanning-tunneling experiments on ${\text{Ca}}_{2\ensuremath{-}x}{\text{Na}}_{x}{\text{CuO}}_{2}{\text{Cl}}_{2}$ by Hanaguri et al. [Science 323, 923 (2009)] observe field-dependent quasiparticle interference effects which are sensitive to the sign of the $d$-wave order parameter. Their analysis of spatial fluctuations in the local density of states shows that there is a selective enhancement of quasiparticle scattering events that preserve the gap sign and a selective depression of the quasiparticle scattering events that reverse the gap sign. We introduce a model which accounts for this phenomenon as a consequence of vortex pinning to impurities. Each pinned vortex embeds several impurities in its core. The observations of recent experiments can be accounted for by assuming that the scattering potentials of the impurities inside the vortex cores acquire an additional resonant or Andreev scattering component, both of which induce gap sign preserving scattering events.