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

Abstract

The carbon monolayer band structure calculated in the approximation of weakly interacting π electrons corresponds to massless electron excitations known as Dirac fermions not previously observed in any other material. However, if strong Coulomb and exchange interactions between π electrons are taken into account, another picture of the π electron state emerges. These interactions result in π electron localization and electron crystal formation. The atomically flat layer can be regarded as a simplest quasi-two-dimensional mesoscopic quantum system consisting of a carbon ion plane and two π electron crystals on opposite sides of the plane. Such a system must have dielectric and pronounced diamagnetic properties and a high sensitivity to external factors distorting its electron crystals. The instability manifests itself in a tendency of the monolayer to be transformed into a more stable carbon modification with a rolled-up or wrapped-up carbon skeleton which is observed as a monolayer corrugation (or ripples). The corrugated monolayer is characterized by the presence of excited π electrons which are responsible for its physical and chemical properties. The approach can prove useful for investigation of carbon nanotubes, fullerenes, graphite, and also topological insulators and complicated quantum systems with a layered structure. Calculations of the quasi-two-dimensional quantum system faces a many-body problem and are beyond the band-structure description, which forces us to confine ourselves to purely qualitative analysis