Dirac Material Graphene

Abstract The paper presents an overview of graphene electronic structure in light of a general concept of emergent phenomena that result from the quantum phase transition caused by continuous symmetry breaking. In the current case, the spin symmetry breaking is provided by a drastic enhancement of pz odd electron correlation when the shortest distance between them, defined by C=C bond length, exceeds critical value Rcri. The UHF formalism clearly evidences the broken symmetry occurrence and perfectly suits to self-consistent description of the issue. Empirically supported and convincingly certified, the UHF emergents, such as (i) open-shell character of electron spinorbitals; (ii) spin polarization of electron spectrum; (iii) spin contamination; (iv) depriving the spin multiplicity of electronic states; (v) local spin pool at zero total spin density, and so forth greatly extend the view on ground states of graphene and other sp2 nanocarbons and not only give a clear vision of spin peculiarities of graphene chemistry but predicatively point to the occurrence of emergents related to graphene physics, such as ferromagnetism, superconductivity and topological nontriviality. The paper presents numerous experimental evidences supporting a deep interrelationship between emergent chemistry and emergent physics of graphene.