Longitudinal and transverse vibration control of electronic conductance of a ladder-like graphene nanoribbon

The coherent electronic transport in a lengthy narrow nanoribbon, which the atoms of a part of it vibrate in some special modes, is modeled analytically within the tight-binding and harmonic approximations. For the small vibrations, the longitudinal and transverse modes are discussed separately. Two in-plane and one out-of-plane vibrating modes are assumed for the vibratory part which is considered as the center wire. The modes which cause the phononic excitations leading to electron-phonon (e-ph) interaction, are chosen in order to present exact analytic formulation. Moreover, we suppose that the bonds in the benzene rings in the center wire are the same or not the same as the rings in the other parts. We found that in-plane atomic vibrations have greater influence on the conductance with respect to the out-of-plane one. Since two conductance channels contribute in the transport, in the overlapping region of their energy bands, the conductance is affected more by the e-ph interaction. Furthermore, the increase electron scattering originating from decrease of electron group velocity, destroys the conductance at the edges of the system energy band.