Patterns induced by magnetic impurities in d-wave superconductors

We investigate the modulated patterns induced by magnetic impurities in d-wave superconductors (DSCs) near optimal doping based on the t-t′-U-V model. Modulated checkerboard patterns with periodicity of eight or four lattice constants (8a or 4a) in the spin-, charge- and DSC orders are observed. Moreover, the checkerboard modulation in the spin order appear to be robust against parameter changes, which is consistent with neutron-scattering experiments. For the two-impurity case, a modulated stripe-like spin order with periodicity 8a is induced, which coexists with the DSC order. Further experiments of magnetic impurity substitution in DSCs are expected to check these results.