Numerical study of the transition to stripe phases in high-temperature superconductors under a strong magnetic field

The nature of the spin density wave (SDW) and charge density wave (CDW) in the mixed state of high-${T}_{c}$ superconductors (HTS) is investigated by using the self-consistent Bogoliubov\char21{}de Gennes equations and an effective model Hamiltonian with competing SDW and d-wave superconductivity interactions. We show that there exists a critical on-site Coulomb interaction ${U}_{c}.$ For optimally doped sample, two-dimensional SDW and CDW modulations are induced for $Ul{U}_{c}$ while SDW and CDW orders become antiferromagnetic (AF) and charge stripes for $Ug{U}_{c}.$ These stripe orders are stabilized and enhanced near the vortex cores. The wavelengths of the AF stripes and charge stripes are found respectively to be $8a$ and $4a,$ with a as the lattice constant. We show that our results could be applied to understand several recent experiments on HTS.