In a simple model we investigate three competing orders: d-wave superconductivity, spin and orbital antiferromagnetism (AF) in the vicinity of a single vortex in a cuprate superconductor. We find that when the potential for the orbital AF V d is comparatively small, the spin-density-wave (SDW) order has an enhancement at the vortex core center, and the "d-density-wave" (DDW) order exhibits a rather weak behavior around the core and vanishing small away from the core. However, when V d becomes large, globally, the SDW order decreases and the DDW order increases; locally, not only the peak of the SDW order around the core still exists, though relatively suppressed, but also a local peak for the DDW order finally appears. Similar effects are also revealed for the features when varying doping. Comparisons with experiments are discussed.
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