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Quantum Interference in Multiwall Carbon Nanotubes

Quantum Interference in Multiwall Carbon Nanotubes. Universität Regensburg. Coworkers and Acknowledgements: B. Stojetz, Ch. Hagen, Ch. Hendlmeier (Regensburg) L. Forró, E. Ljubovic (Lausanne) A. Bachtold , M. Buitelaar, Ch. Schönenberger (Basel) K. Richter, G. Cuniberti (Regensburg)

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Quantum Interference in Multiwall Carbon Nanotubes

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  1. Quantum Interference in Multiwall Carbon Nanotubes Universität Regensburg Coworkers and Acknowledgements: B. Stojetz, Ch. Hagen, Ch. Hendlmeier (Regensburg) L. Forró, E. Ljubovic (Lausanne) A. Bachtold , M. Buitelaar, Ch. Schönenberger (Basel) K. Richter, G. Cuniberti (Regensburg) R. Schäfer (Karlsruhe) Christoph Strunk

  2. multiwalled carbon nanotubes S. Ijima, Nature 354, 56 (1991) 26 nm

  3. Outline Introduction: Electronic structure of carbon nanotubes Quantum interference Changing the electron density Coulomb blockade Perspectives

  4. 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

  5. y x wrapping graphene to nanotubes: RA RB wrapping vector R determines: chirality (real space) allowed k-vectors (k-space)

  6. ky kx Density of states Metallic behavior K K’ K K’ Semicond. behavior

  7. are 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)

  8. 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”

  9. 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”

  10. A. Bachtold et al., ‘98

  11. Similar results obtained by many other groups: Leuven, IBM, Stuttgart, Helsinki …..

  12. E 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 nm

  13. 25 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)

  14. 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

  15. 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 K

  16. Ensemble averaging average weak localization peak survives averaging UCFs averaged out partially, but not completely Stojetz et al., New J. Phys. ‘04 T = 1.7 K(curves shifted)

  17. Weak localization conductance correction due to weak localization: 1.7 K Fitting WL-theory to data: T (K) lf(nm) 1.7 150 20 80 40 50 20 K 40 K effective width W~diameter/2 requiredorigin: flux-cancellation effects ?

  18. Phase coherence length diamonds: UCF measurement triangles: weak localization line: prediction for electron-electron dephasing ~T-1/3elastic mfp: 14 nm  :UCF  :WL Good agreement of lF from WL and UCFs Substantiation of diffusive transport picture Further experiments required to identify origin of disorder

  19. Measure a larger statistical ensemble: shallow conductance minimum at 300K emerging fluctuation pattern at lower T decrease of correlation voltage Vc

  20. Crossover to Coulomb blockade at lowest T : decrease of average conductance Resonant transmission of single channels?

  21. disordered MWNT with irregular Coulomb diamonds: typical capacitances: CGate ~ 55 aF CS ~ 800 aF charging energyEc ~ 100 meV ~ 1.2 K T=30 mK

  22. broad zero bias anomalies remain at higher T: T = 10 K T = 3 K estimated subband spacing ~ 25 meV gate lever arm DEF/UGate ~ 1/10

  23. Magnetoconductance shows pronounced gate dependence: T = 10 K

  24. Open questions Source of disorder -extrinsic or intrinsic ? Strength of disorder? Effect of Coulomb blockage and number of channels on the shape of the WL-peak? Gate dependence of Aharonov-Bohm effect in parallel magnetic field? B

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