Exciton Analog of the Peierls Instability of One‐Dimensional Metals

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Abstract
A one‐dimensional metal in which the conduction electrons interact with excitons in an array of polarizable side groups is shown to possess an inherent instability analogous to the phonon‐induced Peierls instability. The instability manifests itself by the simultaneous appearance of an energy gap at the center of the conduction band and a ferroelectric polarization of the side groups. An approximate quantitative treatment of this effect is presented. The principal conclusions are: (1) the system is unstable for all values of the electron—exciton coupling constant, (2) the resulting semiconducting gap is at least as large as the BCS superconducting gap for the same system, and (3) while it cannot be said with certainty that this precludes superconductivity in such a system it suggests that if it does not become superconducting it will become ferroelectric.

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