Graphene nanoribbon band-gap expansion: broken-bond-induced edge strain and quantum entrapment.

An edge-modified tight-binding (TB) approximation has been developed, enabling us to clarify the energetic origin of the width-dependent band gap (E(G)) expansion of the armchaired and the reconstructed zigzag-edged graphene nanoribbons with and without hydrogen termination. Consistency between the TB and the density-function theory calculations affirmed that: (i) the E(G) expansion originates from the Hamiltonian perturbation due to the shorter and stronger bonds between undercoordinated atoms, (ii) the combination of the edge-to-width ratio with a local bond strain up to 30% and the associated 152% potential well depression determines the width dependent E(G) change; and, (iii) hydrogen termination affects insignificantly the band gap width as the H-passivation minimizes the midgap impurity states.