We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S1, S2) by tunnel junctions. At T = 0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d/vF ≫ ℏ/ΔS, ℏ/ΔCDW where T is temperature. These limits are expressed by using the energy gap in S region ΔS, the length d, the Fermi velocity vF, and the energy gap ΔCDW in CDW region. The critical current is proportional to (ΔCDWℏvF/d)1/2 ∝ ΔCDW(ξCDW/d)1/2. At βΔS(T), βΔCDW(T) ≫ 1 and βℏvF/d ≪ 1, the T-dependence of the correction caused by the phase mode is T-linear where β = 1/kBT and kB is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T. At finite temperatures and without impurities, the critical current is similar to the Ambegaokar-Baratoff formula which is proportional to ΔS(T) in the short-junction limit: d/vF ≪ ℏ/ΔS, ℏ/ΔCDW.
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