  In one dimension the coupling of electrons to phonons leads to a transition
from a metallic to a Peierls distorted insulated state if the coupling exceeds
a critical value. On the other hand, in two dimensions the electron-phonon
interaction may also lead to the formation of Cooper pairs. This competition of
superconductivity and charge order (in conjunction with a lattice distortion)
is studied in this letter by means of the projector-based renormalization
method (PRM). Increasing the electron-phonon interaction, we find a crossover
behavior between a purely superconducting state and a charge-density wave where
a well-defined parameter range of coexistence of superconductivity and lattice
distortion exists.
