Cooper pair and electron-hole pair instabilities in a quasi-one dimensional system

We calculate for an almost half-filled tight-binding band, the mean field ground state energy differences between the charge-density-wave (CDW) and BCS paired states for a truncated model Hamiltonian with zero-range instantaneous electron-electron interactions. The CDW pairing is found to be always unstable vis-à-vis BCS for a static lattice distortion of wave vector Q = (2k_F, π, π).