Magnetic-field-induced spin-density wave in high-temperature superconductors

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 fourfold symmetry. By deceasing doping level, both SDW and CDW show quasi-one-dimensional-like behavior, and the CDW has a period just half of that of the SDW along one direction. From the calculation of the local density of states, 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.