Carbon nanotubes ppt powerpoint11/29/2023 ![]() Magnetoresistance at different gate voltages magnetic field B perpendicular to tube axis magnetoresistance traces taken at various gate voltages (arrows) select different members within statistical ensemble of magneto-fingerprints T = 1.7 KĮnsemble averaging average weak localization peak survives averaging UCFs averaged out partially, but not completely Stojetz et al., New J. Universal conductance fluctuations Interference of many diffusion paths lead to aperiodic fluctuation pattern in the conductance: lF lF > tube diameter (28 nm) lF < tube length (400 nm) Ensemble averaging of conductance fluctuations DGif L < lF vary interference pattern by applying electric or magnetic fields determine phase coherence length lF at different temperatures Similar results obtained by many other groups: Leuven, IBM, Stuttgart, Helsinki ….Į k How to confirm the presence of elastic scattering ? Induce drastic change of electron density by gate electrode (distance 2-3 nm) Change number of current carrying subbands Tune electrochemical potential through charge neutrality point Induce transition between quasi-1dim and strictly 1dim transport ? Au contact Au contact Doping state of MWNTs Effect on weak localization ? Effects of Coulomb interaction ? EF MWNT Al gate (native oxide) 200 nmĢ5 1.7 K 20 5 K R (kW) 10 K 15 15 K 20 K 10 40 K -3 -2 -1 0 1 2 (V) U Gate Gate sweep high temperatures shallow minimum in conductance low temperatures universal conductance fluctuations (UCFs) (curves shifted) ![]() Weak localization and universal conductance fluctuations (UCF) signatures of coherent backscattering in disordered quantum wires: Ai F r’ r Aj Closed loop of time reversed paths: r =r’ F A+ =A- enhanced backscattering probability! Magnetic field breaks time-reversal symmetry: coherent backscattering suppressed by magnetic field: negative magnetoresistance near B=0 reproducible fluctuation pattern specific for impurity configuration: “magneto-fingerprints” Weak localization and universal conductance fluctuations (UCF) signatures of coherent backscattering in disordered quantum wires: Ai r’ r Aj Closed loop of time reversed paths: A+ =A- r =r’ enhanced backscattering probability! Magnetic field breaks time-reversal symmetry: coherent backscattering suppressed by magnetic field: negative magnetoresistance near B=0 reproducible fluctuation pattern specific for impurity configuration: “magneto-fingerprints” behaviorĪre MWNTs ballistic conductors at 300 K? G (2e²/h) z-position (nm) Conductance changes in units of 2e²/h ! Frank, et al., Science 280, 1744 (1998) Ky kx Density of states Metallic behavior K K’ K K’ Semicond. ![]() Y x wrapping graphene to nanotubes: RA RB wrapping vector R determines: chirality (real space) allowed k-vectors (k-space) P* E p ky kx ky kx Graphene: a single sheet of graphite sp2-hybridization leads to planar carbon sheets 2D electronic bandstructure determined by p-orbitals p-bands touch at K-points K K’ G ![]() Outline Introduction: Electronic structure of carbon nanotubes Quantum interference Changing the electron density Coulomb blockade Perspectives Quantum Interference in Multiwall Carbon Nanotubes Universität Regensburg Coworkers and Acknowledgements: B.
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