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We study the effect of electron-phonon (e-ph) interaction on the elastic and inelastic electronic transport of a nanowire connected to two simple rigid leads within the tight-binding and harmonic approximations. The model is constructed using Green's function and multi-channel techniques, taking into account the local and nonlocal e-ph interactions. Then, we examine the model for the gapless (simple chain) and gapped (PA-like nanowire) systems. The results show that the tunneling conductance is improved by the e-ph interaction in both local and nonlocal regimes, while for the resonance conductance, the coherent part mainly decreases and the incoherent part increases. At the corresponding energies which depend on the phonon frequency, two dips in the elastic and two peaks in the inelastic conductance spectra appear. The reason is the absorption of the phonon by the electron in transition into inelastic channels.

A semi-classical model is proposed to explore the effect of electron-phonon coupling on the coherent electronic transport of a polar chain which is confined between two rigid leads in the presence of an external electric field. To this end, we construct the model by means of Green's function technique within the nearest neighbor tight-binding and harmonic approximations. For a time-periodic electric field, the atomic displacements from the equilibrium positions are obtained precisely. The result is then used to compute the electronic transport properties of the chain within the Peierls-type model. The numerical results indicate that the conductance of the system shows interesting behavior in some special frequencies. For each special frequency, there is an electronic quasi-state in which the scattering of electrons by vibrating atoms reaches maximum. The system electronic conductance decreases dramatically at the strong electron-phonon couplings and low electron energies. In the presence of damping forces, the electron-phonon interaction has a less significant effect on the conductance.

We present a theoretical method based on Green’s function technique and tight-binding approach as well as harmonic approximation in order to calculate the coherent electronic conductance of an extended poly(p-phenylene) oligomer in the presence of thermal atomic vibrations. We study two proposed mass-spring models for atomic vibrations: one, including rigid benzene rings connected to each other by vibrating bonds; and in another, the bonds along the oligomer vibrate even in the benzene rings. The electron–phonon (e–ph) interaction influences the electron hopping energies linearly with respect to atomic displacements. The model shows that the conductance spectra exhibit some new energy gaps in the presence of e–ph interaction even at zero temperature. The conductance is more affected by e–ph interaction when the atomic vibrations are supposed to be present in the benzene rings. At the edges of the band energy and central gap, the phonon-assisted phenomena can be observed. Generally, the increasing e–ph interaction strength as well as temperature destroys the electronic conductance especially in the resonance region.