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2009 CARBON ALLOTROPESGraphite from the viewpoint of Landau level spectroscopy: An effectivegraphene bilayer and monolayerThe unusual properties of massless Dirac fermions observedin graphene monolayers, multi-layer epitaxialgraphene or bulk graphite have been extensively studied usingvarious optical and magneto-optical techniques. In contrast,few experiments have addressed the optical responseof a graphene bilayer in spite of the considerable theoreticalinterest into this system. Here we show that some part ofthe physics of the graphene bilayer can be, perhaps surprisingly,studied when investigating bulk graphite.We report on an infrared transmission study of a thin layerof bulk graphite prepared by a multiple exfoliation of anatural graphite crystal, performed in magnetic fields upto B = 34 T. All magneto-transmission spectra were takenin the Faraday configuration with the magnetic field appliedalong the c-axis of the graphite, using technique ofthe Fourier transform spectroscopy.Two series of absorption lines whose energy scales as √ Band B were found in the spectra and identified as contributionsof massless holes at the H point (figure 31a)and massive electrons in the vicinity of the K point (figure.31b), respectively. We have shown that the infraredmagneto-absorption spectra of graphite, measured over awide range of the energy and magnetic field, can be interpretedin a very simple, transparent and elegant manner, i.e.that graphite can be viewed as an effective graphene monolayerand bilayer. Our results thus confirm recent theoreticalmodel [B. Partoens and F. M. Peeters, Phys. Rev. B75, 193402 (2007); M. Koshino and T. Ando, Phys. Rev.B 77, 115313 (2008)], which drastically simplifies the standardSlonczewski-Weiss-McClure model considering onlytwo tight-binding parameters γ 0 and γ 1 , which describe theintra- and inter-layer tunnelling, respectively.In this picture, the dominant contribution to the optical responseis provided by the H point, where electron statesclosely resemble graphene but with an additional doubledegeneracy, and by the K point, where the energy spectrumresembles a graphene bilayer, but with an effective couplingof 2γ 1 , twice enhanced compared to a real bilayer system.Remarkably, using this simple graphene monolayer plus bilayerview of graphite, we are able to correctly reproducethe magnetic field evolution of all observed inter-Landauleveltransitions using only the SWM parameters γ 0 and γ 1 ,with values which perfectly match those derived from studiesof real graphene monolayer and bilayer systems (see figure.31).To conclude, the electronic states at K point of graphite areinterestingly found to mimic those of the graphene bilayer,but with a doubled value of the effective mass. It should benoted that as the validity of the model is limited in the vicinityof the Fermi level, it is not useful, for example, for theinterpretation of magneto-transport experiments. Nevertheless,bulk graphite remains a material of choice to studymagneto-optical phenomena in systems with both masslessas well as massive Dirac fermions.For details see, Orlita et al., Phys. Rev. Lett. 102, 166401(2009) and also Orlita et al., ibid 100, 136403 (2008).Figure 31: (a) Positions of the absorption lines related to theH point as a function of √ B. The solid and dashed lines representexpected positions of absorption lines for ˜c = 1.02 × 10 6 m/s(γ 0 = 3.2 eV). (b) Positions of absorption lines related to the Kpoint as a function of B. The solid lines show expected dipole allowedtransitions in a graphene bilayer with an effective coupling2γ 1 for γ 0 = 3.2 eV and γ 1 = 0.375 eV. The inset schematicallyshows the observed inter-band transitions in the effective bilayer.The gray points in the part (b) have been measured on highly orientedpyrolytic graphite.M. Orlita, C. Faugeras, J. M. Schneider, G. Martinez, D. K. Maude, and M. Potemski23