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A series of carbon allotropes with novel optoelectronic and rich topologicalproperties is predicted by systematic first-principles calculations. Thesefascinating carbon allotropes can be derived by inserting acetylenic linkages(-C$\equiv$C-) into graphite, hence they are termed as grapheaynes. Grapheaynespossess two different space groups, $P$2/$m$ or $C$2/$m$, and containsimultaneously the $sp$, $sp^2$, and $sp^3$ chemical bonds. They have formationenergies lower than the already experimentally synthesized graphdiyne and othertheoretically predicted carbon allotropes with acetylenic linkages.Particularly, when the width $n$ of grapheayne-$n$ exceeds 15, its cohesiveenergy is lower than that of diamond, and approaches that of graphite withincreasing $n$. Remarkably, we find that some grapheaynes behave assemiconductors with direct narrow band gaps and own the highest absorptioncoefficients among all known semiconducting carbon allotropes, while someothers are topological semimetals with nodal lines. Especially, somegrapheaynes can be engineered with tunable direct band gaps in the range of1.07-1.87 eV and have ideal properties for photovoltaic applications. Our worknot only uncovers the unique atomic arrangement and prominent properties of thegrapheayne family, but also offers a treasury that provides promising materialsfor catalyst, energy storage, molecular sieves, solar cell, and electronicdevices.

Grapheayne: a class of low-energy carbon allotropes with diverse optoelectronic and topological properties