Coexistence of superconductivity and charge-density waves in a two-dimensional Holstein model at half-filling

The competition of charge-density waves (CDW) and superconductivity (SC) is studied in a two-dimensional half-filled Holstein model by use of the projector-based renormalization method (PRM). As is well known, in one dimension the coupling of electrons to phonons leads to a transition from a metallic to a Peierls distorted insulated state when the coupling exceeds a critical value. On the other hand, in two dimensions the electron-phonon interaction may also be responsible for the formation of Cooper pairs. In this paper, the competing influence of superconductivity and charge order will be discussed for two dimensions. The PRM not only allows to study SC and CDW correlation functions but gives direct access to the order parameters