Gauge-Invariant Theory of the Dynamical Interaction of Charge Density Waves and Superconductivity

The long-wavelength amplitude mode of the charge-density-wave state modulates the average density of states at the Fermi surface leading to a coupling between it and the order parameter for superconductivity. This is shown, in a gauge-invariant theory, to lead to a bound state below twice the BCS gap. Our results are discussed in the context of recent experiments on $2H$-Nb${\mathrm{Se}}_2$.