Current-voltage characteristics for a tunnel junction composed of a conductor with a CDW and superconductor

Current-voltage (J-V) and differential-conductivity-voltage (dJ/dV-V) characteristics are analytically calculated at zero temperature for a tunnel junction: a superconductor (S) and a Peierls conductor (P) separated by an insulator (I). Here P is a conductor with a charge density wave (CDW). The Hamiltonians of S and P are treated in the mean field approximation. To calculate the current J analytically, Delta (S) = Delta (P) drop Delta is assumed, where Delta (S) and Delta (P) are the energy gaps of S and P, respectively. When the second order of the perturbation theory in the tunnel Hamiltonian is considered in the conventional tunnel Hamiltonian approach, the J-V and dJ/dV-V characteristics depend on only the CDW phase rho. The current J has a discontinuous jump at eV = 2 Delta for rho not equal 0. The differential conductivity dJ/dV has a singularity at eV = 2 Delta for rho not equal 0. The relation J(V, rho) = -J(-V, rho + pi) is obtained.