Vortex Charges in High Temperature Superconductors

Based on an effective model Hamiltonian with competing antiferromagnetic (AF) and d-wave superconductivity (DSC) interactions, the vortex charge in high T_c superconductors is investigated by solving self-consistently the Bogoliubov-de Gennes equations. We found that the vortex charge is always negative when a sufficient strength of AF order is induced inside the vortex core, otherwise, the vortex charge is positive. By tuning the on-site Coulomb repulsion U or the doping parameter $\delta$, a transition between the positive and negative vortex charges may occur. The vortex charge at optimal doping has also been studied as a function of magnetic field. Recent NMR and Hall effect experiments may be understood in terms of the present results. New imaging experiments should be able to probe the vortex charge directly.