We present a tight-binding parametrization for penta-graphene that correctly describes its electronic band structure and linear optical response. The set of parameters is validated by comparing to ab-initio density functional theory calculations for single-layer penta-graphene, showing a very good global agreement. We apply this parameterization to penta-graphene nanoribbons, achieving an adequate description of quantum-size effects. Additionally, a symmetry-based analysis of the energy band structure and the optical transitions involved in the absorption spectra is introduced, allowing for the interpretation of the optoelectronic features of these systems.

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We analyze the symmetry and topological features of a family of materials closely related to penta-graphene, derived from it by adsorption or substitution of different atoms. Our description is based on a novel approach, called topological quantum chemistry, that allows to characterize the topology of the electronic bands, based on the mapping between real and reciprocal space. In particular, by adsorption of alkaline (Li or Na) atoms we obtain a nodal line metal at room temperature, with a continuum of Dirac points around the perimeter of the Brillouin zone. This behavior is also observed in some substitutional derivatives of penta-graphene, such as penta-PC 2 . Breaking of time-reversal symmetry can be achieved by the use of magnetic atoms; we study penta-MnC 2 , which also presents spin-orbit coupling and reveals a Chern insulator phase. We find that for this family of materials, symmetry is the source of protection for metallic and nontrivial topological phases that can be associated to the presence of fractional band filling, spin-orbit coupling and time-reversal symmetry breaking.

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A symmetry analysis combined with first-principles calculations of two-dimensional pentagonal materials (PdSeTe, PdSeS, InP5 and GeBi2) based on the Cairo tiling reveal nontrivial spin textures, nodal lines and Weyl points.

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