Superconductivity close to a charge-density-wave instability

The recent discovery of superconductivity (SC) in proximity of a Peierls distorted phase in the perylene based organic conductor Per$_2$Au(mnt)$_2$ [1] has raised once again the issue about the role of charge-density-wave (CDW) correlations in the mechanism of Cooper pairing. We have applied the renormalization group approach to a quasi-1D model of electrons interacting with acoustic phonons modes and studied the interplay between the two instabilities. From the one-loop flow equations for the momentum and frequency dependent interactions induced by phonons we analyze the stability of CDW and SC states {\it vs} the phonon frequency $\omega_D$ and the hopping parameter $t_\perp'$ for nesting alterations. S-wave SC is demonstrated to be stabilyzed above some critical ${t'}^{*}_\perp$. In these conditions, the superconducting $T_c \sim \omega_D^\eta$ exibits a non-BCS power law increase with $\omega_D$($\eta\simeq 0.7$), as a result of quantum interfering CDW and SC pairings. The complete phase diagram is obtained as a function of both $t_\perp'$ and $\omega_D$ and shown to agree with the one found for Per$_2$Au(mnt)$_2$ under pressure [1]. \medskip \par\noindent [1] D. Graf {\it et al.,} Eur. Phys. Lett. {\bf 85}, 27009 (2009).