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