An Andreev pair from a s-wave superconductor (S) entering a conventionalgapless charge density wave (CDW) below the Peierls gap dephases on the Fermiwavelength 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 sameconclusion holds for averaging over the conduction channels in the ballisticsystem. We apply two microscopic approaches to this phenomenon: i) a Blonder,Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDWinterface; and ii) the Hamiltonian approach for the Josephson effect in a cleanCDW and a CDW with non magnetic disorder. The Josephson effect through a spindensity wave (SDW) is limited by the coherence length, not by the Fermiwave-length.
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