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Exciton energy spectra in polyyne chains

Recently, we have experimentally observed signatures of sharp exciton peaks in the photoluminescence spectra of bundles of monoatomic carbon chains stabilized by gold nanoparticles and deposited on a glass substrate. Here, we estimate the characteristic energies of excitonic transitions in this complex quasi-one-dimensional nano-system with use of the variational method. We show that the characteristic energy scale for the experimentally observed excitonic fine structure is governed by the interplay between the hopping energy in a Van der Waals quasicrystal formed by parallel carbon chains, the neutral-charged exciton splitting and the positive-negative trion splitting. These three characteristic energies are an order of magnitude lower than the direct exciton binding energy.