Raman Response of the Charge Density Wave in Cuprate Superconductors

We study the Raman response, for $B_{1g}$ and $B_{2g}$ light-polarization symmetries, of the charge density wave phase appearing in the underdoped region of cuprate superconductors. We show that the $B_{2g}$ response provides a distinctive signature of the charge order, independently of the details of the electronic structure and from the concomitant presence of a pseudogap, in sharp contrast with the behavior of the $B_{1g}$ response. This well accounts for the Raman experimental results. We then clearly identify a charge density wave energy scale, and show that its doping dependence is eventually driven by the monotonic behavior of the pesudogap. This has also been pointed out in Raman experiments, and it is suggestive of a pseudogap ruling the multiple energy scales of the exotic phases appearing in the cuprate phase diagram.