Dephasing of Andreev pairs entering a charge density wave
  An Andreev pair from a s-wave superconductor (S) entering a conventional gapless charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length, not by the Fermi wave-length. 
S. Duhot and R. M\'elin