Abstract
Within weak-coupling model we construct the superconducting order parameter in the vortex states of the axial and hybrid wave function. In terms of these order parameters the quasi-particle Green's function in the vortex state in the vicinity of upper critical field is constructed. In general the most important modification on the quantum oscillation in the vortex state is increase of the damping constant (or the Dingle temperature). However, since this extra term is proportional to the average of | f |2 over the electron orbit at the belly or neck of the Fermi surface, we find that this exrtra term vanishes for the hybrid state for both [Formula: see text] and [Formula: see text], while it vanishes in the axial state only for [Formula: see text]. This should provide a unique probe to the nature of the superconducting wave functions.
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