One-dimensional exciton in a two-band tight-binding model with long-range interactions

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Abstract
The nature of an exciton in a one-dimensional system is clarified from numerical solutions for the electron-hole attraction varied from the weak (Wannier) limit to strong (Frenkel) limit by making use of a two-band tight-binding model having 1/r as well as on-site interactions. ‘‘Large’’ and ‘‘small’’ excitons are shown to respond to an increase in the strength of the long-range interaction relative to the on-site interaction in opposite manners: the size of an exciton is found to shrink for weak interactions, whereas the extension increases for strong interactions. This property is explained both intuitively and from an exact solution for a simplified model. We further show that the crossover between the large and small excitons should be observable in the optical properties.