  Electronic states around vortex cores in high-Tc superconductors are studied
using the two-dimensional t-J model in order to treat the d-wave
superconductivity with short coherence length and the antiferromagnetic (AF)
instability within the same framework. We focus on the disappearance of the
large zero-energy peak in the local density of states observed in high-Tc
superconductors. When the system is near the optimum doping, we find that the
local AF correlation develops inside the vortex cores. However, the detailed
doping dependence calculations confirm that the experimentally observed
reduction of the zero-energy peak is more reasonably attributed to the
smallness of the core size rather than to the AF correlation developed inside
the core. The correlation between the spatial dependence of the core states and
the core radius is discussed.
