Phase diagram of quasi-one-dimensional metals and superconductivity in the (TMTSF)₂X compounds

The phase diagram of a quasi-one-dimensional metal is derived for a system with interchain tunneling. Retarded and nonretarded forward and backward scattering interactions are included. We show that singly charged acceptor molecules produce a potential along the conducting chains which leads to a retarded umklapp scattering. This umklapp scattering depends strongly on the phonon frequency and can explain the crossover of spin density wave to superconductivity as function of pressure as observed in (TMTSF)₂X compounds.