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.
Piezoelectric Nanotubes (!)
• Electrons on Carbon NT’s
• Heteropolar Nanotubes
• Tubes as Optical Materials
Carbon nanotube contacting
“Long wavelength physics in the extendeddirection is controlled by the short distance physics in the wrapped direction”
• Semiconducting v. Conducting Carbon NT’s
• Pyrolectric and Piezoelectric Effects in III-V’s
• Structure Specific Near Infrared Fluorescence
Dispersion of a free particle in 2D..
by an unconventional E(k) relation on the
The (m,n) wrapping specifies a translation vector of the graphene lattice.
mod(m-n,3) = ±1
mod(m-n,3) = 0, mn
Twist (but not bend) can
on an armchair tube.
this is responsible for
the T-linear observered
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. 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.
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
NT’s are molecular piezoelectrics, where P is
sensitive to twist and stretch, so strain <=>voltage !
Pyroelectric v. Piezoelectric Effects
(topological and discrete)
Strain (short range
and continuously “tunable”)
Piezoelectricity in a Heteropolar Sheet
elastic strain lowers the threefold symmetry of the BN sheet
producing an electric polarization
Elastic Strain on a Heteropolar Tube
Calculated (N-TB) Piezo-Response
• p electron response dominates
• 1/R^2 finite size corrections
• 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 …
Piezoelectricity of Chiral Tubes
From N-TB (calculations for (5,m) (6,m) (12,m) families)
mapped sheet response
Size (R) Scaling of the Piezoelectric
Constants of Chiral Tubes
C, BN NT’s are prototypes with many other compact
meso-phases formed by folding lamellae
double- wall WS2
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)
Physical Properties Control of
Composition AND Geometry
• highly ordered
• access to quantum
systematics in “families”
• control C&G in
• structural sorting
• assembly of networks
Near-infrared Photoluminescence from Single-wall Carbon Nanotubes
Excitation (661 nm)
Emission ( 850 nm)
• 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)
Short Range Interaction
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)