Bridging the Physics and Chemistry of Graphene(s): From Hückel’s Aromaticity to Dirac’s Cones and Topological Insulators

By bridging graphene and benzene through a well-defined sequence of polycyclic aromatic hydrocarbons and their inherent shell structure, it is shown that graphene is actually a coherent arrangement of interwoven benzene molecules, coordinated by aromaticity, shell structure, and topology, all interrelated and microscopically realized through dynamical flipping of the atomic pz-orbitals, playing the role of pseudospin or “qubits”. This renders graphene resonance structure, “resonating” between two complementary aromaticity patterns, involving 2k, k→∞ kekulé type of resonances resulting in “robust electronic coherence”, with dual “molecular-crystalline” nature, and two valence-conduction bands of opposite parity, driven by inversion symmetry competition, which is essentially a “molecule-versus-crystal” competition, in accord with topological-insulator and many-body theory. The “average picture” converges to the usual band structure with two aromatic π-electrons per ring, and the fingerprints of inversion-competition at the D3h-symmetric Dirac points, which for rectangular nanographene(s) appear as gapless topological edge states without real spin-polarization, contrary to opposite claims.