  We study the impact of the Rashba spin-orbit coupling (RSOC) on the stability
of charge-density wave (CDW) in systems with large electron-phonon coupling
(EPC). Here, the EPC is considered in the framework of the Holstein model at
the half-filled square lattice. We start obtaining the phase diagram of the
Rashba-Holstein model using the Hartree-Fock mean-field theory, and identifying
the boundaries of the CDW and Rashba metal phases. As our main result, we
notice that the RSOC disfavors the CDW phase, driving the system to a
correlated Rashba metal. Proceeding, we employ a cluster perturbation theory
(CPT) approach to investigate the phase diagram beyond the Hartree-Fock
approximation. The quantum correlations captured by CPT indicate that the RSOC
is even more detrimental to CDW than previously anticipated. That is, the
Rashba metal region is observed to be expanded in comparison to the mean-field
case. Additionally, we investigate pairing correlations, and the results
further strengthen the identification of critical points.
