Fast Dynamics of the Order Parameter in Superconductors with a Charge-Density Wave

We consider a simple model of a quasi-one-dimensional conductor in which two order parameters (OP) may coexist. These OPs are the superconductingOP ∆ and the OP W that characterizes the amplitude of the charge-density wave (CDW). In the mean field approximation we present equations for the matrix Green’s functionsGik , where the first subscript i relates to the one of the two Fermi sheets and the other, k, operates in the Gor’kov–Nambu space. By using the solutions of these equations, we find the region of coexistence of the OPs ∆ and W at low temperatures T and different values of the parameter μ(p⊥) which describes the curvature of the Fermi sheets. We study the dynamics of the variation of δ∆ and δW in the vicinity of the quantumcritical point whereW turns to zero, and the assumptionW ≪∆ is satisfied. These variations obey two coupled equations for δ∆ and δW . The analytical solutions of these equations are found, and it is shown that there are two characteristic frequencies of oscillations, ω1,2, of the variations δ∆ and δW with ω1 ≃ 2∆ andω2 ≃W . The oscillations with the frequencyω1 decay as cos(2∆t)/ p ∆t .