Peierls instability and superconductivity in quasi-one-dimensional conductors

The transition temperature of the Peierls phase (TP) and of the superconducting phase (Ts) are studied, including a hopping-type interchain coupling and retardation effects due to finite bare phonon frequency ω0. The interactions between the electrons include large and small momentum transfers with attractive couplings s1, s2, respectively. The set of most diverging diagrams is summed and the coexistence line (for which TP=Ts) is shown to be s1=2s2 for the nonretarded interaction. For s12s2 the two phases exclude each other. For a finite (ω)0, increasing (ω)0 is shown to increase Ts while decrease TP. Higher temperatures Ts are possible if (a) ω0 is higher; (b) s1, s2 are stronger, but s1 must stay below a critical value determined by s2 and ω0 (for s2=1, max(Ts)ω020); (c) the commensurate case is avoided; (d) the Peierls instability is suppressed, i.e., by a large enough interchain coupling. The dependence of TP on ω0 implies a positive isotope shift which is measurable if ω02πTP. Such high-frequency phonons are important for high-temperature superconductivity and the isotope shift provides a method for locating them in the Peierls phase.