Lattice Stability and Generation of Massive Dirac Fermions in α-Graphynes and Topological Line Defects in Monolayer BN

Carbon allotropes named α-graphynes (αGy), with sp2 and sp3 bonded carbon atoms (Fig. 1), have been shown to display graphene-like electronic structures with the characteristic Dirac cones. Here, we discuss the lattice stability and gap opening in hydrogenated and oxydized forms of α-graphynes, and show that in both cases, the planar form is unstable against soft-phonon modes with off-plane displacements of hydrogen (oxygen) and carbon atoms. Two mechanisms of mass generation in the Dirac fermion spectrum of α-graphynes are discussed: symmetry breaking and sp 2 -sp 3 rehybridization.