Soft phonon mode and superconducting properties of 2H-NbS2 compared to 2H-NbSe2

I will report on several recent results on 2H-NbS$_{2}$. This compound is the only superconducting 2H-dichalcogenide which does not develop a charge density wave (CDW). I will start with the temperature dependence of the phonon spectra of 2H-NbS$_{2}$ measured by Inelastic X-ray Scattering (IXS). Along $\Gamma$M, a huge softening of two phonon modes was observed on a wide part of the Brillouin zone. This is almost the same as the CDW precursor soft phonons modes that appear above $T_{CDW}\approx33\,K$ in 2H-NbSe${_2}$[Weber11]. It clearly indicates that 2H-NbS$_{2}$ is also at proximity of a CDW instability. In the second part I will show measurement of H$_{c1}$ and magnetic penetration depth, which show signs of a small energy scale in the superconducting gap of 2H-NbS$_{2}$, very similar to 2H-NbSe${_2}$ [Fletcher07], and also in good agreement with STS measurement[Guillamon08]. In view of these two facts and as an open question, we would like to discuss the hypothesis of a quantum critical point (QCP) lying between 2H-NbS$_{2}$ and 2H-NbSe${_2}$, where the 2$^{nd}$ order phase transition would be the CDW instability.