Multi-orbital tight binding model for the electronic and optical properties of armchair graphene nanoribbons in the presence of a periodic potential.

The influences of an external electric field with uniform or modulated potential on the electronic and optical properties of armchair graphene nanoribbons (GNRs) are explored using the multi-orbital tight-binding Hamiltonian. The interplay between an electric field and interaction between (s, $p_x$, $p_y$, $p_z$) orbitals remarkably enriches the main features of band structures and absorption spectra. The applied electric field can notably alter the energy dispersions of $\pi$ and $\sigma$ bands, leading to the deformation of band-edge states, open and close of a band gap, and modification of the Fermi energy. The vertical optical excitations happen among the $\pi$ bands, while their available channels depend on the Fermi level which is controlled by the $\sigma$-edge bands and a finite potential. With the rich and unique properties, GNRs are suitable candidates for applications in the fields of photodetectors, nanoelectronics, and spintronics. The calculated results are expected to be examined by the angle-resolved photoemission spectroscopies (ARPES) and optical spectroscopies.