Controlling electronic and optical properties of zigzag graphene nanoribbons by a modulated electric field: significance of σ bands

We investigate the peculiar electronic and optical properties of zigzag graphene nanoribbons (GNRs) under the effects of uniform and modulated electric fields. The hybridization between the four atomic orbitals (s, px, py, pz) is considered by means of the tight-binding model calculations. Both the π bands originating from the pz orbital and σ bands arising from the (s, px, py) orbitals play critical roles in the electronic structure and thus the absorption spectra. They determine the Fermi level and the available excitation channels between the occupied and unoccupied states. We show that an in-plane electric field in the form of modulated potential can significantly modify the electronic and optical properties of zigzag GNRs. The field-induced modification in energy dispersion, band-edge states, and band gap gives rise to rich absorption spectra with diverse structures. Our theoretical prediction could be verified by angle-resolved photoemission spectroscopies and optical spectroscopies.