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      Density of states and magneto-optical conductivity of graphene in a perpendicular magnetic field

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      Physical Review B
      American Physical Society (APS)

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          Two-Dimensional Gas of Massless Dirac Fermions in Graphene

          Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.
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            Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene

            When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Here, we report an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we observe an unusual half integer QHE for both electron and hole carriers in graphene. Vanishing effective carrier masses is observed at Dirac point in the temperature dependent Shubnikov de Haas oscillations, which probe the 'relativistic' Dirac particle-like dispersion. The relevance of Berry's phase to these experiments is confirmed by the phase shift of magneto-oscillations, related to the exceptional topology of the graphene band structure.
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              Carrier transport in 2D graphene layers

              Carrier transport in gated 2D graphene monolayers is theoretically considered in the presence of scattering by random charged impurity centers with density \(n_i\). Excellent quantitative agreement is obtained (for carrier density \(n > 10^{12} \rm{cm}^{-2}\)) with existing experimental data (Ref. \onlinecite{kn:novoselov2004, kn:novoselov2005, kn:zhang2005, kn:kim2006, kn:fuhrer2006}). The conductivity scales linearly with \(n/n_i\) in the theory, and shows extremely weak temperature dependence. The experimentally observed asymmetry between electron and hole conductivities is explained by the asymmetry in the charged impurity configuration in the presence of the gate voltage, while the high-density saturation of conductivity for the highest mobility samples is explained as a crossover between the long-range and the point scattering dominated regimes. We argue that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for \(n \lesssim n_i \sim 10^{12} \rm{cm}^{-2}\).
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                Author and article information

                Journal
                PRBMDO
                Physical Review B
                Phys. Rev. B
                American Physical Society (APS)
                1098-0121
                1550-235X
                November 2010
                November 18 2010
                : 82
                : 20
                Article
                10.1103/PhysRevB.82.205428
                a90a1555-28f7-4b4a-9695-c3e3c4c74b61
                © 2010

                http://link.aps.org/licenses/aps-default-license

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