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2009 CARBON ALLOTROPESPropagative Landau states and Fermi level pinning in carbon nanotubesCarbon nanotubes (CNT), isolated graphene sheets andgraphene nano-ribbons (GNR) have revealed remarkableelectronic properties. The massless dispersion bands atthe charge neutrality point (CNP) drive spectacular phenomenalike an anomalously low backscattering and relatedlong mean free path in metallic nanotubes, or thehuge charge carriers mobility in graphene layers. CNTand GNR also have in common a large magnetic field dependenceof their 1-D subbands. In graphene, the highmagnetic field behavior of Dirac fermions has been shownto induce an half-integer quantum Hall effect. In singleand multi-walled carbon nanotubes (MWCNT), whileAharonov-Bohm phenomena were investigated in-depth foraxial magnetic fields, the exploration of Landau states inpresence of high transversal magnetic fields has been facingoverwhelming technical challenges. On the theoreticalside, a drastic change of the 1-D dispersion bands hasbeen predicted once the cyclotron radius equals the tuberadius. The calculations show that the resulting magneticbands remain dispersive along the tube axis at large k wavevectorssuggesting an inhomogeneous chiral current flowingat the flanks of the tube. At low k-vectors, a Landau levelsspectrum is derived with the √ nB magneto-fingerprintof graphene, whatever the CNT chirality. Notwithstanding,an experimental spectroscopy of Landau states in CNTshas not yet been achieved and the longitudinal magnetoconductancein the quantum regime remains unexplored.In this work, MWCNTs of diameters in the range of 10 nmto 20 nm are selected to reach the high magnetic fieldregime under 60 T, corresponding to a dimensionless parameterν = r/l B larger than 1 (r is the tube’s radius andl B = √ /eB, the magnetic length). In the following, wefocus on two MWCNTs whose external shells, mainly contributingto the conductance, have been identified respectively,as behaving as semiconducting and metallic shells,in the light of their Aharonov-Bohm magneto-fingerprints[Nanot et al., C. R. Physique 10, 268 (2009)].The contribution of propagative Landau states to magnetotransportin semiconducting and metallic MWCNTshells is experimentally unveiled [Nanot et al., submitted].For semiconducting shells, the occurrence of a zeroenergyLandau state associated with the energy gap closureis found to generate strongly delocalized states closeto the Dirac point, despite the presence of disorder andlow dimensionality, and irrespective of the electrostaticdoping strength. For doped metallic shells, the magnetoconductancealso exhibits an upshift of the massive 1Dbandsin agreement with the formation of Landau states.At the CNP, the re-introduction of the backscattering inthe metallic bands, clearly evidences the onset of the zeroenergyLandau state (figure 4). Even more spectacular isthe pinning of the Fermi level at the CNP in high field(figure 5). These remarkable features are supported byLandauer-Büttiker simulations of the magnetoconductanceof weakly disordered semiconducting and metallic CNTs.Figure 4: High magnetic field perpendicular magneto-conductanceobtained at 100 K on a individually connected MWCNT forvarious Fermi energies. The drastic decrease of the conductanceabove 25 T results from the re-introduction of the back-scatteringalong with the onset of the first Landau level at zero energy.Figure 5: Landauer-Büttiker simulation of the perpendicularmagneto-conductance on a (10,10) NTC in presence of weak disorderfor various magnetic field dependent electrostatic potentials.The magenta curve with cross marks is the calculated magneto–conductance at a fixed Fermi energy. In inset, the magnetic fielddependence of the electrostatic potential illustrating the so calledpinning of the Fermi energy at the charge neutrality point.S. Nanot, W. Escoffier, J-M Broto, B. Raquet,S. Roche, R. Avriller (Commissariat à l’Energie Atomique, INAC, SP2M, Grenoble)7