  Quantum-dot states in graphene nanoribbons (GNR) were calculated using
density-functional theory, considering the effect of the electric field of gate
electrodes. The field is parallel to the GNR plane and was generated by an
inhomogeneous charge sheet placed atop the ribbon. Varying the electric field
allowed to observe the development of the GNR states and the formation of
localized, quantum-dot-like states in the band gap. The calculation has been
performed for armchair GNRs and for armchair ribbons with a zigzag section. For
the armchair GNR a static dielectric constant of {\epsilon} approx. 4 could be
determined.
