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The carbon monolayer band structure calculated in the approximation of weaklyinteracting {\pi} electrons corresponds to massless electron excitations knownas Dirac fermions not previously observed in any other material. However, ifstrong Coulomb and exchange interactions between {\pi} electrons are taken intoaccount, another picture of the {\pi} electron state emerges. Theseinteractions result in {\pi} electron localization and electron crystalformation. The atomically flat layer can be regarded as a simplestquasi-two-dimensional mesoscopic quantum system consisting of a carbon ionplane and two {\pi} electron crystals on opposite sides of the plane. Such asystem must have dielectric and pronounced diamagnetic properties and a highsensitivity to external factors distorting its electron crystals. Theinstability manifests itself in a tendency of the monolayer to be transformedinto a more stable carbon modification with a rolled-up or wrapped-up carbonskeleton which is observed as a monolayer corrugation (or ripples). Thecorrugated monolayer is characterized by the presence of excited {\pi}electrons which are responsible for its physical and chemical properties. Theapproach can prove useful for investigation of carbon nanotubes, fullerenes,graphite, and also topological insulators and complicated quantum systems witha layered structure. Calculations of the quasi-two-dimensional quantum systemfaces a many-body problem and are beyond the band-structure description, whichforces us to confine ourselves to purely qualitative analysis

Atomically flat carbon monolayer as an extremely unstable quasi-2D mesoscopic quantum system