On the Origin of Quantum Oscillations in the Mixed State of Anisotropic   Superconductor
  For the vortex lattice in an anisotropic superconductor with well-separated cores (Hc1<<B<<Hc2) it is shown that sizable de Haas-van Alphen oscillations are caused by the levels` crossing of the energy threshold separating localized and extended states of excitations moving in the average magnetic field,B. 
Lev P. Gor`kov