The exciton model of superconductivity in linear chains — revisited
We present a detailed calculation of the transition temperature of a model, filamentary excitonic superconductor. The proposed structure consists of a linear chain of transition-metal atoms to which is complexed a ligand system of highly polarizable dye molecules. The model is discussed in the light of recent developments in our understanding of one-dimensional metals. We show that for the structure proposed, the momentum dependence of the exciton interaction results in the superconducting state being favoured over the Peierls state, and in vertex corrections to the electron -exciton interaction which are small. The calculation of the transition temperature is based on what we believe to be reasonable estimates of the strength of the excitonic interaction, Coulomb repulsion and band structure. For the particular model proposed, transition temperature of several hundred degrees are calculated. However, we find superconductivity only in systems in which the excitonic medium is within a covalent bond length of, and completely surrounds the conductive spine. This imposes severe constraints on the structure of any excitonic superconductor.