Analytical study of the ballistic transport of ladder-like graphene nanoribbons within the tight-binding approach

• Analytic formalism for electronic transport of ladder-like graphene nanoribbons.
• Using Green’s function technique in the tight-binding approach.
• Applying the formalism on brunched and un-brunched nanoribbons.

We analytically study the electronic transport properties of ladder-like graphene nanoribbons using Green’s function method within the tight-binding approach. We first renormalize the system to have a uniform ladder network with energy dependent tight-binding parameters. Then, we convert the ladder network into two independent uniform simple chains by separating its Hamiltonian modes. Next, we calculate the density of states and transmission coefficient of the considered nanoribbons by employing the corresponding exact analytical formulas related to a uniform chain. Finally, we apply this formalism to some different configurations of brunched and un-brunched nanoribbons and discuss the electron tunneling through such structures. It turns out that in the un-brunched cyclic nanoribbons the electron tunnels easier than the brunched cyclic ones in the center wire gap regions.