Theoretical Chemistry of α-Graphyne: Functionalization, Symmetry Breaking, and Generation of Dirac-Fermion Mass

We investigate the electronic structure and lattice stability of pristine and functionalized (with either hydrogen or oxygen) α-graphyne systems. We identify lattice instabilities due to soft-phonon modes and describe two mechanisms leading to gap opening in the Dirac-Fermion electronic spectrum of these systems: symmetry breaking, connected with the lattice instabilities, and partial incorporation of an sp 3 -hybrid character in the covalent-bonding network of a buckled hydrogenated α-graphyne lattice that retains the symmetries of the parent pristine α-graphyne. In the case of an oxygen-functionalized α-graphyne structure, each O atom binds asymmetrically to two twofold-coordinated C atoms, breaking inversion and mirror symmetries, and leading to the opening of a sizable gap of 0.22 eV at the Dirac point. Generally, mirror symmetries are found to suffice for the occurrence of gapless Dirac cones in these α-graphyne systems, even in the absence of inversion symmetry centers. Moreover, we analyze the gapless and gapped Dirac cones of pristine and functionalized α-graphynes from the perspective of the dispersion relations for massless and massive free Dirac Fermions. We find that mirror-symmetry breaking mimics a Dirac-Fermion mass-generation mechanism in the oxygen-functionalized α-graphyne, leading to gap opening and to isotropic electronic dispersions with a rather small electron–hole asymmetry. In the hydrogen-functionalized case, we find that carriers show a remarkable anisotropy, behaving as massless Fermions along the M – K line in the Brillouin zone and as massive Fermions along the Γ – K line.