The two-dimensional Rashba-Holstein model

In this work, we investigate the role of Rashba spin-orbit coupling in charge density wave and superconducting states on a square lattice at half-filling. Employing the finite-temperature determinant Quantum Monte Carlo method, we scrutinize the Holstein model to investigate the effects of Rashba spin-orbit coupling on the evolution of change density wave and also superconducting states in the antiadiabatic limit. As a result, we show that the ground state charge density wave phase is not destroyed when the Rashba spin-orbit coupling parameter $\alpha$ is increasing. In addition, in a pure Rasbha spin-orbit coupling regime, where the hopping parameter is absent, we found a rich phase diagram with Weyl semimetal for low values of electron-phonon coupling and consequent transition to change density wave states for high intensities of electron-phonon coupling. Furthermore, a presence of a coexistence of superconducting and charge density wave states for a high phonon frequency and electron-phonon coupling.