2009 CARBON ALLOTROPESElectric field doping of few-layer graph<strong>en</strong>eThe electronic properties of few-layer graph<strong>en</strong>e have be<strong>en</strong>investigated at low temperature and high magnetic field.Few-layer graph<strong>en</strong>e systems consist of a few t<strong>en</strong>s of planesof carbon atoms stacked upon each others and exhibit acomplex electronic band structure. Regarding their transportproperties, they are natural candidates to study thecross over from 3D graphite to 2D graph<strong>en</strong>e. So far, manystudies have focused on graph<strong>en</strong>e, where a linear dispersionrelation at the K and K ′ points of the first Brillouin zoneleads to transport properties governed by massless quasiparticles.Such charge carrier dynamic makes graph<strong>en</strong>ea unique 2D system and is responsible, among other, tothe anomalous quantum Hall effect. On the other hand,graphite supports the pres<strong>en</strong>ce of differ<strong>en</strong>t groups of chargecarriers (electron-like and hole-like quasi-particles), amongwhich massless Dirac fermions have already be<strong>en</strong> reported[Luk’yanchuck et al. Phys. Rev. Lett., 93, 166402 (2004)].The experim<strong>en</strong>tal investigation of few-layer graph<strong>en</strong>e hasbe<strong>en</strong> undertak<strong>en</strong> in an attempt to determine the relative contributionsof the differ<strong>en</strong>t types of charge carriers to electronictransport, in a system where a small number of carbonlayers makes its electronic properties half-way betwe<strong>en</strong>those of graphite and graph<strong>en</strong>e.+70 V shows a monotonously increasing function with nohint of resistance maximum. We therefore infer that thesample is intrinsically p-doped and that the charge neutralitypoint is out of the experim<strong>en</strong>tal range. Contaminantsand/or defects are responsible for shifting the charge neutralitypoint away from V g = 0 V.Figure 24: 3D plot of the Hall resistance R xy as a function ofmagnetic field B and gate voltage V gFigure 23: Oscillatory part of R xx (B,V g ) after subtracting asmooth background function. For clarity, the curves are shiftedvertically by 1.5 kΩThe few-layer graph<strong>en</strong>e sample is obtained by exfoliationof bulk graphite and deposited onto a heavily dopedSi/SiO 2 substrate with 300 nm oxide thickness. Fourelectro<strong>des</strong> have be<strong>en</strong> fabricated on the sample using photolithographyso that the two-probe longitudinal and Hallresistance could be simultaneously measured during a pulseof the magnetic field. A gate voltage is applied thoughthe SiO 2 dielectric in order to continuously tune the chargecarrier d<strong>en</strong>sity. As compared to the simple plane capacitormodel usually accepted for graph<strong>en</strong>e, the few-layergraph<strong>en</strong>e system displays reduced gate effici<strong>en</strong>cy, mostprobably due to large scre<strong>en</strong>ing effects. The gate voltagedep<strong>en</strong>d<strong>en</strong>ce of the resistance in the range −70 < V g
CARBON ALLOTROPES 2009Low temperature magneto-transport in natural graphiteHistorically, graph<strong>en</strong>e forms the starting point for the Slonczewski,Weiss and McClure (SWM) band structure calculationsof graphite. In graphite, the Bernal stacked graph<strong>en</strong>elayers are weakly coupled with the form of the in-planedispersion dep<strong>en</strong>ding upon the mom<strong>en</strong>tum k z in the directionperp<strong>en</strong>dicular to the layers. The carriers occupy a regionalong the H − K − H edge of the hexagonal Brillouinzone. At the K point (k z = 0), the dispersion of the electronpocket is parabolic (massive fermions), while at the H point(k z = 0.5) the dispersion of the hole pocket is linear (masslessDirac fermions). A clear signature of Dirac fermionsat the H point of graphite has rec<strong>en</strong>tly be<strong>en</strong> reported usingfar-infrared magneto-absorption and ARPES measurem<strong>en</strong>ts.Such measurem<strong>en</strong>ts probe the very close vicinity ofthe H and K points where there is a maximum in the jointd<strong>en</strong>sity of states.Typical low temperature R xx versus magnetic field for naturalgraphite, is shown in Fig. 25(a). The quantum oscillations,superimposed on a large magneto-resistance background,can be better se<strong>en</strong> in the background removed data∆R xx plotted in Fig. 25(a-c). Quantum oscillations are observedfor both majority electrons and holes with orbitalquantum number up to almost N = 100. These oscillationsare fully consist<strong>en</strong>t with the pres<strong>en</strong>ce of majority electronand hole pockets within the three dim<strong>en</strong>sional SWM bandstructure calculations for graphite [Schneider et al. Phys.Rev. Lett. 102, 166403 (2009)]. At low magnetic fields,a perfect linear behavior in N(1/B) is observed for bothelectrons and holes. For high magnetic fields, clear deviationsfrom the linear behavior are observed for the electronfeatures (see Fig. 26(b-c)). This deviation from a periodicin 1/B behavior at high magnetic fields is due to theFermi level moving as the quantum limit is approachedin graphite. Clearly, the high field data should not beused to extract the phase of the oscillations. Instead weuse the complex Fourier transform ˆf (B) of the low magneticfield ∆R xx (1/B). The phase shift function K(ϕ,B) =Re[e −iϕ ˆf (B)] has maximum in the ϕ − B plane which canbe used to extract both the frequ<strong>en</strong>cy (B) and phase (ϕ) ofthe oscillations. K(ϕ,B) is plotted in Fig. 26(d-e) in theregions of the hole and electron features. From the maxima,the determined frequ<strong>en</strong>cy and phase are B fh = 4.51 T,ϕ h = −(0.56±0.1)π and B fe = 6.14 T, ϕ e = −(0.86±0.1)πfor the hole and electron features respectively.We therefore conclude that we have no evid<strong>en</strong>ce for theexist<strong>en</strong>ce of masseless Dirac fermions with a Berry phaseγ = 0. Transport measurem<strong>en</strong>ts are s<strong>en</strong>sitive to the d<strong>en</strong>sityof states at E F , which is modulated with increasing magneticfield, as the Landau bands cross the Fermi <strong>en</strong>ergy. Forholes, maxima in the d<strong>en</strong>sity of states correspond to Landaubands crossing E F for k z < 0.5, away from the H point,where the dispersion is no longer linear and a priori there isno reason to expect the carriers to behave as Dirac fermions.Figure 25: (a) Resistance R xx versus B measured at T = 10 mKfor natural graphite. (a-c) Background removed data ∆R xx showingquantum oscillations measured over differ<strong>en</strong>t magnetic fieldregions. The arrows indicate spin split electron and hole features.Figure 26: (a) Fourier transform of the low magnetic field∆R xx (1/B). (b-c) Orbital angular mom<strong>en</strong>tum quantum numberN, as a function of the reciprocal magnetic field positions of theelectron and hole features. (d) and (e) Contour plot of the phaseshift function K(ϕ,B) in the vicinity of the hole and electron features.Maxima in K(ϕ,B) determines the frequ<strong>en</strong>cy and phase ofthe oscillations.J. M. Schneider, M. Orlita, M. Potemski and D. K. Maude20
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2009 MAGNETIC SYSTEMSY b 3+ → Er
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2009 MAGNETIC SYSTEMSMagnetotranspo
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2009 MAGNETIC SYSTEMSHigh field tor
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2009 MAGNETIC SYSTEMSNuclear magnet
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2009 MAGNETIC SYSTEMSStructural ana
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2009 MAGNETIC SYSTEMSEnhancement ma
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2009 MAGNETIC SYSTEMSInvestigation
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2009 MAGNETIC SYSTEMSField-induced
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2009 MAGNETIC SYSTEMSMagnetic prope
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2009Biology, Chemistry and Soft Mat
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BIOLOGY, CHEMISTRY AND SOFT MATTER
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2009 APPLIED SUPERCONDUCTIVITYMagne
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2009 APPLIED SUPERCONDUCTIVITYPhtha
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2009Magneto-Science105
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MAGNETO-SCIENCE 2009Study of the in
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MAGNETO-SCIENCE 2009Magnetohydrodyn
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MAGNETO-SCIENCE 2009112
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 PROPOSALSProposals for Magnet
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2009 PROPOSALSSpin-Jahn-Teller effe
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2009 PROPOSALSQuantum Oscillations
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2009 PROPOSALSThermoelectric tensor
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2009 PROPOSALSDr. EscoffierCyclotro
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2009 PROPOSALSHigh field magnetotra
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2009 THESESPhD Theses 20091. Nanot
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2009 PUBLICATIONS[21] O. Drachenko,
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2009 PUBLICATIONS[75] S. Nowak, T.
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Contributors of the LNCMI to the Pr
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Institut Jean Lamour, Nancy : 68Ins
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Lawrence Berkeley National Laborato