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Graphene & Graphite

Recently graphene, a single sheet of graphite, was discovered. Graphene is the first truly two-dimensional system which exhibits unique electronic properties mostly related to its peculiar band structure. The remarkable physics exhibited by graphene has its origin in the conduction and the valence bands which meet at the two inequivalent (K and K0) corners of the Brillouin zone. The electrons in the vicinity of the Fermi energy do not obey Schrodinger’s equation, but should instead be described using the quantum-electrodynamic Dirac equation for relativistic fermions with zero rest mass. The electrons have a linear dispersion relation whose slope defines a Fermi velocity vF . In a relativistic analogy, these electrons behave as massless Dirac fermions moving at an effective speed of light vF . Moreover, graphene is a gapless material. This system is of great interest from a fundamental physics point of view and it has even been suggested that graphene can be used for bench top quantum electrodynamics experiments, for example to test the Klein paradox .

Graphite - Magnetotransport

Recently, massless Dirac fermions have been observed at the K point of the Brillouin zone in graphene, a hexagonally arranged carbon monolayer with quite extraordinary properties. Historically, graphene forms the starting point for the Slonczewski, Weiss and McClure (SWM) band structure calculations of graphite. In graphite, the Bernal stacked graphene layers are weakly coupled with the form of the in-plane dispersion depending upon the momentum kz in the direction perpendicular to the (...)

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Graphite – de Haas van Alphen to probe the Fermi surface

The Fermi surface of graphite has electron and hole majority carrier pockets with maximal extremal cross sections at kz=0 (electrons) kz =0.35 (holes). For both types of charge carriers the in-plane dispersion is parabolic (massive fermions). Only at the H point (kz=0.5) the in-plane dispersion is linear, similar to that of charge carriers in graphene (massless Dirac fermions). At the H-point,there are two possible extremal orbits. A minimal (neck) orbit of the majority hole carriers, which (...)

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Graphite – Electron-Hole asymmetry of optical transitions

Graphite has been extensively investigated in particular, magneto-optical techniques have been used to probe the energy spectrum at the H and K-points where there is a joint maximum in the optical density of states. Within the effective bi-layer model for graphite, with only two parameters, the observed splitting of the K-point transitions in the magneto-reflectance data was described by including the electron-hole asymmetry due to the non vertical coupling term phenomenologically. (...)

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