Harrison Model of Polyynic Carbyne Chains

The electronic properties of finite and infinite polyynic carbyne chains have been investigated using the tight-binding Hamiltonian of the Harrison’s model and the Green’s function method. By considering all of the atomic orbitals, the energy band structure of a polyyne chain has been numerically evaluated by the system’s Hamiltonian resulting from the discretized form of the Schrödinger’s equation. The obtained results show that due to dimerization and/or bond length alternation which cause an energy bandgap, the polyynic carbyne exhibits a semiconductive or even insulating behavior. Without dimerization, the carbyne displays the characteristics of a conductor. On the basis of the precise comparative study of the measured results, the band gaps of finite and infinite polyynes with the same bond length alternation are nearly equal to each other. Therefore, a polyyne chain (finite or infinite) under mechanical strain can be exploited as a device with adjustable bandgap. The results are in a good overall agreement with the recent experimental findings and further expand some of the previous theoretical results.