Electron, phonon, and thermoelectric transport properties of a-, b-, c-, and 6,6,12-graphyne sheets are compared and contrasted with those of graphene. a-, b-, and 6,6,12-graphynes, with direction dependent Dirac dispersions, have higher electronic transmittance than graphene. c-graphyne also attains better electrical conduction than graphene except at its band gap. Vibrationally, graphene conducts heat much more efficiently than graphynes, a behavior beyond an atomic density differences explanation. Seebeck coefficients of the considered Dirac materials are similar but thermoelectric power factors decrease with increasing effective speeds of light. c-graphyne yields the highest thermoelectric efficiency with a thermoelectric figure of merit as high as ZT ¼ 0.45, almost an order of magnitude higher than that of graphene. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4902920] Graphene and its functionalized forms have many extraordinary physical properties, such as robustness, stability, flexibility, very high thermal, and electrical conductivities, 1-8 which inspired numerous studies exploring the possibilities for adapting them for technological applications in the fields of not only electronics, photonics, and optoelectronics, 9-11 but also thermoelectrics and thermal management of nano-devices. 8,[12][13][14][15][16][17][18] Recently, it was shown that other two-dimensional materials can also be stable and that they widen the potential of two-dimensional materials for applications. [19][20][21][22] Of particular importance are graphene-like carbon allotropes, called graphyne structures composed of one-atom-thick sheets of carbon atoms but containing sp carbon bonds in addition to sp 2 hybridized bonds 23-25 (see Fig. 1). Indeed, assembled subunits of several graphyne structures 26-28 and another similar graphene allotrope including triple-bonded carbon linkages, so-called graphdiyne films and nanoribbons have already been synthesized. 29,30 Theoretical calculations have shown that these lowdimensional structures have unique mechanical, 24,31-33 thermal, 34,35 optical, 36 and particularly electrical [37][38][39][40][41][42] properties as peculiar as those of graphene. For instance, 6,6,12-graphyne, exhibit direction-dependent conductivity due to its electronic structure possessing two self-doped nonequivalent distorted Dirac cones. 38 On the other hand, c-graphyne has a direct energy band gap, 43,44 which is appealing for electronic applications. 45 Considering that one of the most important concerns about graphene is the difficulty to manipulate its electronic conduction due to absence of a band gap, c-graphyne was argued to be more suitable for electronics. 46 More recently, thermoelectric properties of graphynes were reported to have interesting features. 35,47,48 Yet, the potential of graphynes for applications require further investigations.In this work, electronic, phononic, and thermoelectric transport properties of four types of graphyne structures, namely, a-, b-, c-, and 6,6,12-graphynes,...