Influence of electric and magnetic fields and σ -edge bands on the electronic and optical spectra of graphene nanoribbons

The unusual electronic and optical properties of armchair and zigzag graphene nanoribbons (GNRs) subject to in-plane transverse electric and perpendicular magnetic fields have been systematically investigated. Our calculations were carried out within the generalized multiorbital tight-binding model based on a Hamiltonian which takes into account hopping integrals among the ($s,\phantom{\rule{0.28em}{0ex}}{p}_{x},\phantom{\rule{0.28em}{0ex}}{p}_{y}$, and ${p}_{z}$) atomic orbitals as well as the external electric and magnetic fields. The electronic structure consists of $\ensuremath{\pi}$ bands arising from the ${p}_{z}$ orbital and $\ensuremath{\sigma}$ bands originating from the ($s,\phantom{\rule{0.28em}{0ex}}{p}_{x}$, and ${p}_{y}$) orbitals. The energy bands and optical spectra are diversified by both the nature of the edge of the nanoribbon and the strength of the external fields. Armchair GNRs display a width-dependent energy gap in addition to low-energy $\ensuremath{\sigma}$ bands whereas the zigzag system has the unfilled flatband with $\ensuremath{\pi}$ edge states at zero energy and partially filled wide-range $\ensuremath{\sigma}$ bands. An applied in-plane electric field leads to the splitting of energy bands and shifted Fermi level thereby enriching the interband and intraband optical conductivities. The interplay between an external magnetic field and the edge geometry gives rise to extraordinary quantized Landau levels and special optical spectra.