Friedel oscillation in charge profile and position dependent screening around a superconducting vortex core.

We calculate microscopically the charge distribution around a vortex in type II superconductors by solving the Bogoliubov-de Gennes equation and the Poisson equation simultaneously. Our calculations show that the charge density depletion occurs in the vortex center and the Friedel oscillation appears over the coherence length when k(F)xi is small. We also calculate the density-density correlation function K(r,r(')) as a function of two spatial variables, r and r('), and find that K(r,r(')) is strongly dependent on the distance from the vortex center. We clarify the spatial dependent screening properties on the basis of the correlation function in the core region.