Abstract
The induction of spin density wave (SDW) and charge density wave (CDW) orderings in the mixed state of high $T_c$ superconductors (HTS) is investigated by using the self-consistent Bogoliubov-de Gennes equations based upon an effective model Hamiltonian with competing SDW and d-wave superconductivity interactions. For optimized doping sample, the modulation of the induced SDW and its associated CDW is determined by the vortex lattice and their patterns obey the four-fold symmetry. By deceasing doping level, both SDW and CDW show quasi-one dimensional like behavior, and the CDW has a period just half that of the SDW along one direction. From the calculation of the local density of states (LDOS), we found that the majority of the quasi-particles inside the vortex core are localized. All these results are consistent with several recent experiments on HTS.
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