  The present work deals with the study of d-wave superconductor in presence of
a single vortex placed at the centre of the 2D lattice using the $t-t'-J$ model
within the renormalized mean field theory. It is found that the in absence of
the vortex the ground state has a d-wave configuration. In presence of the
vortex, the superconducting order parameter, above the critical doping, drops
to a low non zero value within a few lattice points from the vortex (that is
within the the vortex core) and beyond it converges to the constant value in
absence of vortex. We observe that above the critical doping things are
consistent with the experimental results while there is an anomalous rise in
the superconducting order parameter at very low doping within the vortex core.
This we feel is because of antiferromagnetic ordering taking place within the
vortex core at low doping.
