Epitaxial Carbyne: Analytical Results

The Green's function method in the tight-binding approximation is used to obtain analytical expressions for the electronic spectra and densities of states for two carbyne structural modifications (cumulene and polyyne). Metal and semiconductor substrates are considered and charge-transfer estimates are deduced. Criteria for the occurrence of a charge-density wave in free-standing and epitaxial carbynes are proposed taking into account the intra- and interatomic Coulomb repulsion. Analytical expressions for the phonon spectrum of free-standing carbyne are presented. The data obtained are compared with the results of numerical calculations performed by other researchers.