Peierls instability and superconductivity in quasi-one-dimensional conductors

Abstract

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 ${\ensuremath{\omega}}_{0}$. The interactions between the electrons include large and small momentum transfers with attractive couplings ${s}_{1}$, ${s}_{2}$, respectively. The set of most diverging diagrams is summed and the coexistence line (for which ${T}_{P}={T}_{s}$) is shown to be ${s}_{1}=2{s}_{2}$ for the nonretarded interaction. For ${s}_{1}\ensuremath{\ne}2{s}_{2}$ the two phases exclude each other. For a finite ${(\ensuremath{\omega})}_{0}$, increasing ${(\ensuremath{\omega})}_{0}$ is shown to increase ${T}_{s}$ while decrease ${T}_{P}$. Higher temperatures ${T}_{s}$ are possible if (a) ${\ensuremath{\omega}}_{0}$ is higher; (b) ${s}_{1}$, ${s}_{2}$ are stronger, but ${s}_{1}$ must stay below a critical value determined by ${s}_{2}$ and ${\ensuremath{\omega}}_{0}$ (for ${s}_{2}=1$, $max({T}_{s})\ensuremath{\simeq}\frac{{\ensuremath{\omega}}_{0}}{20})$; (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 ${\ensuremath{\omega}}_{0}$ implies a positive isotope shift which is measurable if ${\ensuremath{\omega}}_{0}\ensuremath{\gtrsim}2\ensuremath{\pi}{T}_{P}$. Such high-frequency phonons are important for high-temperature superconductivity and the isotope shift provides a method for locating them in the Peierls phase.