  We investigate the spectrum of quasiparticle excitations in the core of
isolated pancake vortices in clean layered superconductors. Analysis of the
spectral current density shows that both the circular current around the vortex
center as well as any transport current through the vortex core is carried by
localized states bound to the core by Andreev scattering. Hence the physical
properties of the core are governed in clean high-$\kappa$ superconductors
(e.g. the cuprate superconductors) by the Andreev bound states, and not by
normal electrons as it is the case for traditional (dirty) high-$\kappa$
superconductors.
