Coherence in the Quasi-Particle 'Scattering' by the Vortex Lattice in Pure Type-II Superconductors

Abstract

The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the de-Haas van-Alphen oscillations in a pure type-II superconductor is investigated within mean field,asymptotic perturbation theory. Using a 2D electron gas model it is shown that, due to a strict phase coherence in the many-particle correlation functions, the 'scattering' effect in the asymptotic limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted by the random vortex lattice model proposed by Maki and Stephen, which destroys this coherence . The coherent many particle configuration is a collinear array of many particle coordinates, localized within a spatial region with size of the order of the magnetic length. The amplitude of the magnetization oscillations is sharply damped just below $% H_{c2}$ because of strong $180^{\circ}$ out of phase magnetic oscillations in the superconducting condensation energy ,which tend to cancel the normal electron oscillations. Within the ideal 2D model used it is found, however, that because of the relative smallness of the quartic and higher order terms in the expansion, the oscillations amplitude at lower fields does not really damp to zero, but only reverses sign and remains virtually undamped well below $H_{c2}$. This conclusion may be changed if disorder in the vortex lattice, or vortex lines motion will be taken into account. The reduced QP 'scattering' effect may be responsible for the apparent crossover from a strong damping of the dHvA oscillations just below $H_{c2}$ to a weaker damping at lower fields observed experimentally in several 3D superconductors.