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 SourceDrainGate

3. “Long wavelength physics in the extended direction 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. The (m,n) wrapping specifies a translation vector of the graphene lattice. Rolling-up a graphene sheet m=nmod(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))  P is obtained from the geometric (Berry’s) phase accumulated by the u’s under adiabatic motion on a closed orbit in  -space.

10. Nanotube Polarization as a Geometric Phase Control parameters: q x, ,  with valence eigenstates that adiabatically follow  sum over states and integrate over  to obtain

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

12. The magnitude of the dipole is sensitive to elastic strain (modulate  ) 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 stretchtwist 3m symmetry:

15. Elastic Strain on a Heteropolar Tube stretch twist armchairzigzag

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

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

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

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

20. Photogalvanic Effects in Heteropolar Tubes

21. C, BN NT’s are prototypes with many other compact meso-phases formed by folding lamellae MoS 2 Remska et al. Science 292, 479 (2001) WS 2 Single- and double- wall WS 2 coat C-NT and WS 2 cones Whitby et al. APL 79, 4574 (2001) & many others: Tenne & Zettl, Topics. In Applied Physics 80, 81 (2001)

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

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. The “deviations problem” They are very large… with ± asymmetry Curvature, Trig. Warping + Coul. Anisotropy (distinguished by scaling with R, n) Long Range Interaction 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)