Far infrared transmission experiments are performed on ultrathin epitaxial graphite samples in a magnetic field. The observed cyclotron resonance-like and electron-positron-like transitions are in excellent agreement with the expectations of a single-particle model of Dirac fermions in graphene, with an effective velocity ofc = 1.03×10 6 m/s. The electronic properties of graphite have recently become the center of considerable attention, following experiments on graphite monolayers (graphene) [1] and epitaxial graphene [2], which led to the discovery of an unusual sequence of quantum Hall effect states [3,4] and an energy-dependent mass. The considerable interest in two-dimensional graphite is fuelled by its particular band structure and ensuing dispersion relation for electrons, leading to numerous differences with respect to "conventional" two-dimensional electron systems (2DES) [2,5,6,7,8,9,10,11,12]. The band structure of graphene is considered to be composed of cones located at two inequivalent Brillouin zone corners at which the conduction and valence bands merge. In the vicinity of these points the electron energy depends linearly on its momentum: E( − → p ) = ±c| − → p |, which implies that free charge carriers in graphene are governed not by Schrödinger's equation, but rather by Dirac's equation for zero rest mass particles, with an effective velocityc, which replaces the speed of light. With the application of an external magnetic field, the Dirac energy spectrum evolves into Landau levels with energies given bywhere n scans all positive (for electrons) and negative (for holes) integers and -very importantly -zero. E 1 may be understood as a characteristic energy introduced by the magnetic field. The square root dependence on B and Landau level index n is in stark contrast to "conventional" 2D electrons, where E n = (n+ 1 2 ) eB/m, (n ≥ 0), and the Landau levels are equally spaced.The unusual sequence of quantum Hall effect states and an energy-dependent electron effective mass [3,4], found in magneto-resistance measurements, are consistent with the model of Dirac particles. Here we report a magneto-spectroscopy study of the optical properties of ultrathin epitaxial graphite layers, in which we directly probe the dependence of the energy of electrons on their momentum.The experiments were performed on graphene layers grown in vacuum by the thermal decomposition method [2,12], on single crystal (4H) SiC. These epitaxial graphene structures are routinely characterized using low energy electron diffraction, Auger electron spectroscopy, X-ray diffraction, scanning tunnelling microscopy and atomic force microscopy. The results of these measurements in combination with angular resolved photoelectron spectroscopy and transport data indicate that the graphitized part of this type of structure consists of a few (3-5) graphene layers [2,12]. We investigated two such (unpatterned) structures, with dimensions of about 4 x 4 mm 2 , which both show a similar behavior.The far infra-red transmission of the samples wa...
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We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low-energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However, at higher energies (>500 meV) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is approximately 40 meV. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.
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