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Striped morphologies induced by magnetic impurities in d-wave superconductors

We study striped morphologies induced by magnetic impurities in d-wave superconductors (DSCs) near optimal doping by self-consistently solving the Bogoliubov-de Gennes equations based on the $t-t^{\prime }-U-V$ model. For the single impurity case, it is found that the stable ground state is a modulated checkerboard pattern. For the two-impurity case, the stripe-like structures in order parameters are induced due to the impurity-pinning effect. The modulations of DSC and charge orders share the same period of four lattice constants (4$a$), which is half the period of modulations in the coexisting spin order. Interestingly, when three or more impurities are inserted, the impurities could induce more complex striped morphologies due to quantum interference. Further experiments of magnetic impurity substitution in DSCs are expected to check these results.