  We argue that inhomogeneity inherent to the presence of periodic
supercurrents in the vortex lattice sorts excitations by energies into the ones
that are spatially localized and those that perform motion along large Larmour
orbits. This energy threshold results in a new mechanism for the de Haas-van
Alphen oscillations which enhances oscillations at B<<Hc2, even for an
isotropic superconductor with a constant gap. We suggest that the mechanism is
of a general character and can cause the slow decay of the de Haas-van Alphen
effect when the field, B, decreases below Hc2.
