  We present a detailed study of vortex core spectroscopy in slightly overdoped
Bi2Sr2CaCu2O8 using a low temperature scanning tunneling microscope. Inside the
vortex core we observe a four-fold symmetric modulation of the local density of
states with an energy-independent period of (4.3\pm 0.3)a0. Furthermore we
demonstrate that this square modulation is related to the vortex core states
which are located at ~6 meV. Since the core-state energy is proportional to the
superconducting gap magnitude, our results strongly suggest the existence of a
direct relation between the superconducting state and the local electronic
modulations in the vortex core.

Superconductivity;Strongly Correlated Electrons