Peierls instability and superconductivity in quasi-one-dimensional conductors

The transition temperature of the Peierls phase (T_P) and of the superconducting phase (T_s) 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 T_P=T_s) is shown to be s₁=2s₂ for the nonretarded interaction. For s₁≠2s₂ the two phases exclude each other. For a finite (ω)₀, increasing (ω)₀ is shown to increase T_s while decrease T_P. Higher temperatures T_s 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, (T_s)~=ω₀20) (c) the commensurate case is avoided; (d) the Peierls instability is suppressed, i.e., by a large enough interchain coupling. The dependence of T_P on ω₀ implies a positive isotope shift which is measurable if ω₀>~2πT_P. Such high-frequency phonons are important for high-temperature superconductivity and the isotope shift provides a method for locating them in the Peierls phase.