γ-graphdiyne is a two-dimensional (2D) carbon structure beyond graphene: it is formed by $sp$ and $s{p}^2$ carbon atoms organized as hexagonal rings connected by linear links, and it is predicted to be a semiconductor. The lateral confinement of γ-graphdiyne nanoribbons significantly affects the electronic and vibrational properties. By means of periodic density-functional theory (DFT) calculations we here investigate the electronic band structure, the Raman and IR spectra of γ-graphdiyne 2D crystal and related nanoribbons. We discuss the effect of the functional and basis set on the evaluation of the band gap, highlighting the reliability of hybrid functionals. By joining DFT calculations with a symmetry analysis, we assign in detail the IR and Raman spectra of γ-graphdiyne. On this basis we show the modulation of the gap in nanoribbons of increasing width and different edges (armchair, zigzag). We assess how confinement affects the Raman and IR spectra by comparing vibrational modes with phonons of the parent 2D crystal. Our symmetry-based classification allows identifying the marker bands sensitive to the edge structure and lateral confinement of nanoribbons of increasing width. These results show the effectiveness of vibrational spectroscopy for the characterization of such nanostructures.

• Received 26 September 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.4.014001