Graphite related materials such as graphene have been extensively studied in recent years due to their exceptional electronic, optoelectronic, and mechanical properties. One-dimensional Graphene NanoRibbons (GNRs) are recognized as promising building blocks for nanoelectronic devices. Quantum confinement in GNRs introduces a tunable bandgap suitable for electronic and optical applications.
To study the optical properties of GNRs an accurate model of the bandstructure is needed. The electronic bandstructure of Armchair GNRs (AGNRs) can be obtained by discretizing the transverse wavenumber in accordance with the edge boundary condition. Analytical models for the dispersion relation and the wave functions of AGNRs are available in the literature. For Zigzag GNRs (ZGNRs), however, a compact model for the electronic bandstructure cannot be derived because the transverse wavenumber also depends on the longitudinal wavenumber. We present two approximations for the wavenumber of ZGNRs, which result in simple analytical expressions for the bandstructure and wave functions. We show that the analytical model is valid for a wide range of GNR widths. Based on this model, selection rules for optical transitions and optical properties of ZGNRs are obtained.
Transition rules and optical properties of AGNR embedded in hexagonal boron nitride lattices have been studied for the first time. Based on tight-binding calculations considering first and second nearest neighbors, we have shown that the optical transition rules of such structures are completely different from that of conventional GNRs. The optical spectrum, the quantum efficiency, and the photoresponsivity of different nanoribbons have been evaluated and their application in photodetectors investigated. The results obtained were in excellent agreement with first principles calculations.