Transation of charged vortex structures in underdoped high-temperature superconductors

Vortex structures in high-temperature superconductors are studied by solving Bogoliubov-de Gennes equations based on a mean-field t-t′-U-V-Vc model. The results show that transition from checkerboard pattern to stripe structure for spin density wave, charge density wave, and d-wave orderings may occur by enhancing the strength of the on-site repulsion U. When a reasonable long-range Coulomb interaction is introduced into the model Hamiltonian, two-dimensional modulations or the checkerboard patterns may appear for the underdoped samples, which is consistent with the scanning-tunneling-microscopy experiments.