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 p-orbitals, playing the role of pseudospins or "qubits". This renders graphene resonance structure, "resonating" between two complementary aromaticity patterns, involving 2, → ∞ Kekulé type of resonances, resulting in "robust electronic coherence", with a 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 accordance with topological insulators and many-body theory. The "average picture" converges to the usual band structure with two aromatic π-electrons per ring, and with the fingerprints of inversion competition at the -symmetric Dirac points, which for rectangular nanographene(s) appear as gapless topological edge states without real spin polarization, in contrast to opposite claims.