We investigate the behavior of the Higgs (amplitude) mode when
superconductivity emerges on a preexisting charge-density-wave state. We show
that the weak overdamped square-root singularity of the amplitude fluctuations
in a standard BCS superconductor is converted in a sharp, undamped power-law
divergence in the coexisting state, reminiscent of the Higgs behavior in
Lorentz-invariant theories. This effect reflects in a strong superconducting
resonance in the Raman spectra, both for an electronic and a phononic mechanism
leading to the Raman visibility of the Higgs. In the latter case, our results
are relevant to the interpretation of the Raman spectra measured experimentally
in NbSe2.Comment: Extended version, accepted for publication in PR
