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Bottom-up synthesis from molecular precursors is a powerful route for thecreation of novel synthetic carbon-based low-dimensional materials, such asplanar carbon lattices. The wealth of conceivable precursor moleculesintroduces a significant number of degrees-of-freedom for the design ofmaterials with defined physical properties. In this context, a priori knowledgeof the electronic, vibrational and optical properties provided by modern abinitio simulation methods can act as a valuable guide for the design of novelsynthetic carbon-based building blocks. Using density functional theory, weperformed simulations of the electronic properties of armchair-edged graphenenanoribbons (AGNR) with a bisecting 4-8 ring defect line. We show that theelectronic structures of the defective nanoribbons of increasing width can beclassified into three distinct families of semiconductors, similar to the caseof pristine AGNR. In contrast to the latter, we find that every thirdnanoribbon is a zero-gap semiconductor with Dirac-type crossing of linear bandsat the Fermi energy. By employing tight-binding models including interactionsup to third-nearest neighbors, we show that the family behavior, the formationof direct and indirect band gaps and of linear band crossings in the defectivenanoribbons is rooted in the electronic properties of the individual nanoribbonhalves on either side of the defect lines, and can be effectively throughintroduction of additional 'interhalf' coupling terms.

Family behavior and Dirac bands in armchair nanoribbons with 4-8 defect lines