Dispersion of superconducting gap excitations in layered charge density wave systems

The phonon spectral function for charge density wave (CDW) systems in the superconducting (SC) phase is calculated for finite wave vectors (q). An exact expression for the q dependent phonon self-energy is obtained. The analysis is carried out with a small q limit. The spectral function shows a two peak structure for frequencies co less than the SC energy gap (2Δ) in contrast to the single peak obtained by Balseiro and Falicov for q = 0. The peaks approach each other with increasing q and finally merge into one. Both modes have linear dispersions for small q and the frequency of the low-lying one goes to zero as q → 0. For ω > 2Δ the phonon spectrum does not change significantly. The results are discussed in context with the Raman scattering observation of SC gap excitations in 2H–NbSc2 (a layered compound exhibiting both CDW and SC transitions) by Sooryakumar and Klein. The present calculation demands that the strength of coupling between the CDW phonon and SC electrons be an order of magnitude smaller than that used for q = 0 in order to get an agreement with the experimental result.