Ab initio calculations indicate that topological-defect networks in graphene display the full variety of single-particle electronic structures, including Dirac-fermion null-gap semiconductors, as well as metallic and semiconducting systems of very low formation energies with respect to a pristine graphene sheet. Corrugation induced by the topological defects further reduces the energy and tends to reduce the density of states at the Fermi level, to widen the gaps, or even to lead to gap opening in some cases where the parent planar geometry is metallic.
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