Influence of electric and magnetic fields and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>?</mml:mi></mml:math> -edge bands on the electronic and optical spectra of graphene nanoribbons

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