Nonstationary Josephson effect for superconductors with charge-density waves

The nonstationary Josephson I¹, interference I², and quasiparticle J currents through symmmetrical and nonsymmetrical tunnel junctions involving superconductors with charge-density waves (CDW's) were calculated. In the symmetrical (s) case the voltage V dependence of the Josephson current I_s¹(V) has logarithmic singularities at |eV|=2Δ,fΔ+D, and 2D, where D=√(Δ²+Σ²), Δ is the superconducting order parameter, Σ is the dielectric order parameter, and e is the elementary charge. For temperatures T≠0 the jump at a bias |eV|=D-Δ emerges in I_s¹(V). The I_s²(V) and J_s(V) possess jumps and singularities at the same biases where singularities and jumps occur in I_s¹(V). For the nonsymmetrical (ns) junctions, which include also the ordinary superconductor, singularities and jumps appear at biases |eV|=D+Δ_BCS, Δ +Δ_BCS, and (for T≠0) |D-Δ_BCS| and |Δ-Δ_BCS|. Here Δ_BCS is the superconducting order parameter of the ordinary superconductor. The quasiparticle current J_ns is an asymmetrical function of the voltage V and depends on the sign of Σ. The theory describes the properties of NbSe₃ and high-T_c oxides.