Vortex lattice melting and the damping of the dHvA oscillations in the mixed state

Phase fluctuations in the superconducting order parameter, which are responsible for the melting of the Abrikosov vortex lattice below the mean field $H_{c2}$, are shown to dramatically enhance the scattering of quasi-particles by the fluctuating pair potential, thus leading to enhanced damping of the dHvA oscillations in the liquid mixed state. This effect is shown to quantitatively account for the detailed field dependence of the dHvA amplitude observed recently in the mixed state of a Quasi 2D organic SC.