Impurity and fluctuation effects in charge-density-wave superconductors

Abstract

We formulate a theory of a charge-density-wave (CDW) distorted superconductor, in the presence of impurities and CDW fluctuations. This theory is expected to be applicable to the layered compound $2H$-Nb${\mathrm{Se}}_{2}$. Our primary aim is to compute the superconducting density of states ${N}_{s}(\ensuremath{\omega})$. We also obtain the temperature dependence of the order parameter $\ensuremath{\Delta}$. We show, when all other parameters are fixed, that nonmagnetic impurities will raise the superconducting transition temperature and $\ensuremath{\Delta}$. Since the CDW gap ${W}_{Q}$ is expected to decrease with concentration, this effect should be even more pronounced. For nonmagnetic impurities, ${N}_{s}(\ensuremath{\omega})$ is found to be "BCS-like" with a gap at $\ensuremath{\Delta}\ensuremath{\ne}{\ensuremath{\Delta}}^{\mathrm{BCS}}$, with subsidiary structure at $\ensuremath{\omega}={({\ensuremath{\Delta}}^{2}+{W}_{Q}^{2})}^{\frac{1}{2}}$. As the nonmagnetic impurity concentration is further increased this structure rounds out and ${N}_{s}(\ensuremath{\omega})$ approaches the strict BCS limit. CDW fluctuation effects are expected to lead to fine structure in ${N}_{s}(\ensuremath{\omega})$ at the characteristic phonon frequency. In principle, an analysis of (future) tunneling data will give detailed information about the CDW excitations, some of which has been obtained from Raman spectroscopy.