Vortex Pattern and Local Density of States in High-Temperature Superconductors with Different Hole-Doped Level

Vortex charges in high-temperature superconductors (HTS) with a different hole-doped level are investigated by Bogoliubov-de Gennes equations based on a model Hamiltonian with competing antiferromagnetic (AFM) and d-wave superconducting order (DSC). Our results show that the AFM order inside the vortex core becomes significant for the underdoped sample, which competes with the DSC order through expulsion of the holes from outside the vortex core and leads to a negative vortex charge, whereas the vortex charge shows a double-vortex center with a positively charged core and a negatively charged core for a slightly overdoped level; and the positive vortex charge may occur for a highly hole-doped level. Moreover, local density of states indicates that the presence of the AFM order in the vortex core provides a mechanism for splitting of the zero-bias conductance peak into local peaks at the core center.