Abstract
We investigate the coupling of the collective modes of a coexistent incommensurate charge-density-wave (CDW) superconductor (SC). We use a gauge-invariant random-phase approximation that correctly includes screening to treat both the amplitude and phase modes of the coupled system. Unlike previous work, the SC and CDW orderings are treated fully self-consistently, on an equal footing, and it is found that the only significant coupling is between the CDW and SC amplitude modes. We obtain qualitative agreement with Raman scattering data on Nb${\mathrm{Se}}_{2}$. The phase modes should not display any new structure in addition to that corresponding to pure CDW and pure superconducting order.
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