Piezoelectric Nanotubes Electrons on Carbon NTs Heteropolar 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
“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)
Graphene has a Critical Electronic State Dispersion of a free particle in 2 D. . …is replaced by an unconventional E(k) relation on the graphene lattice
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
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.
Are Nanotubes Photogalvanic ?
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
Quantum Theory of Polarization (King-Smith & Vanderbilt, Phys. Rev. B 47, 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.
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
The NT’s electric dipole moment that depends on its wrapping
The magnitude of the dipole is sensitive to elastic strain (modulate d) NT’s are molecular piezoelectrics, where P is sensitive to twist and stretch, so strain <=>voltage !
Pyroelectric v. Piezoelectric Effects Geometrical (topological and discrete) (physics) Strain (short range and continuously “tunable”) (chemistry)
Piezoelectricity in a Heteropolar Sheet elastic strain lowers the threefold symmetry of the BN sheet producing an electric polarization stretch 3 m symmetry: twist
Elastic Strain on a Heteropolar Tube armchair stretch twist zigzag
Calculated (N-TB) Piezo-Response of Nanotubes sheets zigzag armchair N-TB DFT • p electron response dominates • 1/R^2 finite size corrections
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 … stretch twist
Piezoelectricity of Chiral Tubes From N-TB (calculations for (5, m) (6, m) (12, m) families) mapped sheet response tube mapped sheet response
Size (R) Scaling of the Piezoelectric Constants of Chiral Tubes
Photogalvanic Effects in Heteropolar Tubes
C, BN NT’s are prototypes with many other compact meso-phases formed by folding lamellae Mo. S 2 WS 2 Single- and double- wall WS 2 coat C-NT and WS 2 cones Whitby et al. APL 79, 4574 (2001) Remska et al. Science 292, 479 (2001) & many others: Tenne & Zettl, Topics. In Applied Physics 80, 81 (2001)
Physical Properties Control of Composition AND Geometry challenges • control C&G in synthesis • structural sorting • assembly of networks and superstructures opportunities • highly ordered (coherent) structures • access to quantum geometrical effects • phenomenology: systematics in “families”
Near-infrared Photoluminescence from Single-wall Carbon Nanotubes Excitation (661 nm) Emission ( 850 nm)
Fluorescence Spectroscopy • FS reveals electronic gap structure outside the conventional band model. • The “ratio problem” Gap Ratio < 2 (asymptote for large diameter tubes) Long Range Interaction Hybridize e-h and 2 e-2 h excitations 1 D + degeneracy from tube wrapping. • The “deviations problem” Short Range Interaction They are very large… with ± asymmetry Curvature, Trig. Warping + Coul. Anisotropy (distinguished by scaling with R, n)
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.
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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