Physics and chemistry of graphene. Emergentness, magnetism, mechanophysics and mechanochemistry

Graphene is considered 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 continuous symmetry. This review starts by examining the spin symmetry breaking of the graphene electron subsystem caused by the correlation of its odd $\rm {p_z}$-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 magnitude $R_{\rm cr}$=1.395 Å. The symmetry breaking is reliably predicted by the unrestricted Hartree–Fock (UHF) formalism, which 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) a spin-mixed ground state and, as a consequence, violation of the exact spin multiplicity of electronic states, and (iv) the existence of local spins at zero total spin density. Using this approach greatly expands our understanding of the ground state of graphene and other $\rm sp^{2}$ 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 for both the spin system and time reversal and imposes on 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.