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Piezoelectric Nanotubes (!)

Piezoelectric Nanotubes (!). • Electrons on Carbon NT’s • Heteropolar Nanotubes Pyroelectricity Piezoelectricity Photogalvanics • Tubes as Optical Materials. ….with Na Sai Charlie Kane Petr Kral. Carbon nanotube contacting platinum electrodes. Gate. Source. Drain.

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Piezoelectric Nanotubes (!)

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  1. Piezoelectric Nanotubes (!) • Electrons on Carbon NT’s • Heteropolar Nanotubes Pyroelectricity Piezoelectricity Photogalvanics • Tubes as Optical Materials ….with Na Sai Charlie Kane Petr Kral

  2. Carbon nanotube contacting platinum electrodes Gate Source Drain

  3. “Long wavelength physics in the extendeddirection is controlled by the short distance physics in the wrapped direction” Some examples • Semiconducting v. Conducting Carbon NT’s • Pyrolectric and Piezoelectric Effects in III-V’s (this work) • Structure Specific Near Infrared Fluorescence (in progress)

  4. Graphene has a Critical Electronic State Dispersion of a free particle in 2D.. …is replaced by an unconventional E(k) relation on the graphene lattice

  5. Rolling-up a graphene sheet The (m,n) wrapping specifies a translation vector of the graphene lattice. m=n mod(m-n,3) = ±1 mod(m-n,3) = 0, mn

  6. Backscattering from elastic strains: bend and twist Twist (but not bend) can backscatter electrons on an armchair tube. this is responsible for the T-linear observered resistivity.

  7. Are Nanotubes Photogalvanic ?

  8. Heteropolar NT’s of Boron Nitride BN is the III-V homolog to graphene. The B and N occupy different sublattices -- this lowers the symmetry and leads to new physical effects

  9. Quantum Theory of Polarization (King-Smith & Vanderbilt, Phys. Rev. B47, 1651 (1993)) DP is obtained from the geometric (Berry’s) phase accumulated by the u’s under adiabatic motion on a closed orbit in t-space.

  10. Nanotube Polarization as a Geometric Phase Control parameters: qx, d, D with valence eigenstates that adiabatically follow W sum over states and integrate over D to obtain

  11. The NT’s electric dipole moment that depends on its wrapping

  12. The magnitude of the dipole issensitive to elastic strain (modulate d) NT’s are molecular piezoelectrics, where P is sensitive to twist and stretch, so strain <=>voltage !

  13. Pyroelectric v. Piezoelectric Effects Geometrical (topological and discrete) Strain (short range and continuously “tunable”) (physics) (chemistry)

  14. Piezoelectricity in a Heteropolar Sheet elastic strain lowers the threefold symmetry of the BN sheet producing an electric polarization stretch twist 3m symmetry:

  15. Elastic Strain on a Heteropolar Tube armchair zigzag stretch twist

  16. Calculated (N-TB) Piezo-Response of Nanotubes zigzag armchair sheets N-TB DFT • p electron response dominates • 1/R^2 finite size corrections

  17. Chiral Tubes • Chiral tubes have a wrapping vector  high symmetry translation of the BN sheet (chiral angle q). • Electric Dipole couples to both stretch and torsion bilinear stretch-twist coupling! • Low Symmetry  Large Unit Cell, but … twist stretch

  18. Piezoelectricity of Chiral Tubes From N-TB (calculations for (5,m) (6,m) (12,m) families) mapped sheet response mapped sheet response tube

  19. Size (R) Scaling of the Piezoelectric Constants of Chiral Tubes

  20. Photogalvanic Effects inHeteropolar Tubes

  21. C, BN NT’s are prototypes with many other compact meso-phases formed by folding lamellae MoS2 WS2 Single- and double- wall WS2 coat C-NT and WS2 cones Whitby et al. APL 79, 4574 (2001) & many others: Tenne & Zettl, Topics. In Applied Physics 80, 81 (2001) Remska et al. Science 292, 479 (2001)

  22. Physical Properties  Control of Composition AND Geometry challenges opportunities • highly ordered (coherent) structures • access to quantum geometrical effects • phenomenology: systematics in “families” • control C&G in synthesis • structural sorting • assembly of networks and superstructures

  23. Near-infrared Photoluminescence from Single-wall Carbon Nanotubes Excitation (661 nm) Emission ( 850 nm)

  24. Fluorescence Spectroscopy • FS reveals electronic gap structure outside the conventional band model. • The “ratio problem” Gap Ratio < 2 (asymptote for large diameter tubes) Hybridize e-h and 2e-2h excitations 1D + degeneracy from tube wrapping. Long Range Interaction • The “deviations problem” They are very large… with ± asymmetry Curvature, Trig. Warping + Coul. Anisotropy (distinguished by scaling with R, n) Short Range Interaction

  25. Stick Boy and Match Girl Stick Boy liked Match Girl he liked her a lot. He liked her cute figure, he thought she was hot.

  26. But could a flame ever burn for a match and a stick? It did quite literally; he burned up pretty quick. children’s poetry by Tim Burton (1997)

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