Graphene is considered as a specific object whose electronic structural features are presented in the light of the general concept of emergent phenomena that arise as a result of a quantum phase transition caused by the breaking of a continuous symmetry. This review starts by examining the spin symmetry breaking of the graphene electronic system caused by the correlation of its odd pz electrons that depends on the distance between these electrons and becomes noticeable when the shortest distance, determined by the C=C bond length, exceeds the critical value Rcr=1,395 Å. The symmetry breaking is reliably predicted by universal Hartree—Fock (UHF) formalism that provides a sufficient level of quantitative self-consistent description for the problem. Empirical support has been given to and reliable certification obtained for UHF emergents such as (i) open-shell electron spin-orbitals; (ii) splitting and/or spin polarization of electron spectra; (iii) spin-mixed ground state and, as a consequence, violation of the exact spin multiplicity of electronic states; (iv) existence of local spins at zero total spin density. Using this approach greatly expands our understanding of the ground state of graphene and other sp2 nanocarbons and not only gives a clear insight into the spin features of graphene chemistry, accentuating its emergent character, but also expectedly predicts the occurrence of new graphene physics related emergents. In the latter case, symmetry breaking is relevant not only for spin systems but also for time reversal and imposes to graphene special physical properties such as ferromagnetism, superconductivity and topological nontriviality. This review shows, for the first time, that not only the ferromagnetism but also the mechanical properties of graphene are essentially emergent, extending this feature to the entire physics of graphene.
Keywords: graphene, graphane, open-shell molecules, emergent phenomena, spin symmetry breaking, universal Hartree—Fock (UHF) quantum-chemical approach, Dirac quasi-relativistic approach, hexagonal honeycomb structure, Dirac fermions, spin-orbital coupling, local spins, time reversal symmetry breaking, topological nontriviality, high temperature ferromagnetism, interfacial superconductivity, mechanical properties, static deformation, dynamic deformation, covalent bonds PACS:62.25.−g, 68.65.Pq, 73.22.Pr (all) DOI:10.3367/UFNe.2017.11.038233 URL: https://ufn.ru/en/articles/2018/7/b/ Citation: Sheka E F, Popova N A, Popova V A "Physics and chemistry of graphene. Emergentness, magnetism, mechanophysics and mechanochemistry" Phys. Usp.61 645–691 (2018)