Electron-libron modes in a quasi-one-dimensional conductor

A model calculation is done so as to study the conduction-electron excitation spectrum for a solid consisting of equally spaced atoms which are free to rotate about their centers of mass. In this model, the atoms are assumed to be electrically neutral dipoles of spin $\frac{1}{2}$. Owing to the Coulomb interaction between an electron and a libron (the quantum of libration) on neighboring lattice sites, it is shown that the system possesses a bound excitonic state consisting of an electron and a libron. The quasiparticle spectrum for the excitons consists of two branches ${\omega }_k^{(\pm )}$ which are labeled by the wave number $k$. The gap function ${\Delta }_k$, which is a measure of the electron-libron pairing, and a parameter $\eta$, determining the orientational order for the atomic system, are determined by a set of coupled equations. We study the conditions under which there are electron-libron modes by doing numerical calculations for various values of the parameters.