Electronic states around a vortex core in high-T_c superconductors based on the t-J model

Electronic states around vortex cores in high-T_c 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-T_c superconductors. When the system is near the optimum doping, we find that the local AF correlation develops inside the vortex cores. However, 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.