Based on a model Hamiltonian with competing antiferromagnetic (AF) and $d$-wave superconductivity interactions, the vortex charge is investigated by solving the Bogoliubov–de Gennes equations. We found that the vortex charge is negative when a sufficient strength of AF order is induced inside the vortex core; otherwise, it 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.

• Received 28 June 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.217001