Spin and Charge Order around Vortices and Impurities in High-T_c Superconductors

A comparative study is made for the spin and charge structure around superconducting vortices and unitary impurities, by solving self-consistently an effective Hamiltonian including interactions for both antiferromagnetic spin-density wave (SDW) and d-wave superconducting orderings. Around vortices, we show the induction of an SDW two-dimensionally modulated with a period of eight lattice constants (8a₀) and an associated charge-density wave (CDW) with a period of 4a₀, which explains very well recent experimental observations. In the case of unitary impurities, an SDW modulation with identical periodicity, but without an associated CDW, is also predicted.