Magnetic quantization of electronic states in d-wave superconductors

We derive a general quasiclassical approach for long-range magnetic-field quantization effects in superconductors. The method is applied to superclean d-wave superconductors in the mixed state. We study the delocalized states with energies $\epsilon \gg \Delta_{0}\sqrt{H/H_{c2}}$. We find that the energy spectrum consists of narrow energy bands whose centers are located at the Landau levels calculated in absence of the vortex potential. We show that transitions between the states belonging to the different Landau levels give rise to resonances in the a.c. quasiparticle conductivity and in the a.c. vortex friction.