Harrison Model of Polyynic Carbyne Chains

Abstract

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.

Calculation of Electron Transport in Short Polyyne Nanochains

“…1,11,27,66 Therefore, a polyyne nanochain (under mechanical strain) can be exploited as a nanodevice with tunable bandgap. 31 The shape of TP curves as a function of the injecting electron energy  (divided by t p p 2 z z ) with considering only one AO and all kinds of AOs are depicted in Fig. 4 by using Eq.…”

“…The DOS of a system describes the number of states that are available to be occupied by the system at each level of energy. 31,55,61 The electron TP through the polyyne nanodevice in NEGF formalism is calculated by using the Fisher-Lee relation 62…”

“…11,27,28 The symmetric cumulenes are expected to exhibit metallic behavior, due to the homogeneous distribution of the π-electrons over the nanochain, while the broken-symmetry polyynes are semiconductors, as a result of BLA. 6,[29][30][31] In accordance with the Peierls effect, 32 the cumulenic carbyne should immediately distort to the alternate polyynic configuration and hence be unstable. Since the energetic stability difference between the cumulenic perfect structure and the polyynic distorted structure is relatively insignificant, both 1D structures can coexist under suitable experimental conditions.…”