Modulations of orders around magnetic impurities in high-temperature superconductors

By using a model Hamiltonian with competing antiferromagnetic (AFM) spin density wave (SDW) and d-wave superconductivity orders, the spin and charge structures around magnetic impurities in high-temperature superconductors is investigated. We find one-dimensional stripe and two-dimensional checkerboard-like modulations of orders around a magnetic impurity. A phase diagram of next-nearest-neighbor hopping strength |t′| versus AFM interaction U for various patterns of orders in the presence or absence of a magnetic impurity is given. Moreover, the impurity-induced stripe orders can transit to two-dimensional modulations for smaller impurity strength.