Piezoelectric Nanotubes

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Piezoelectric Nanotubes (!)
Electrons on Carbon NTs Heteropolar
Nanotubes Pyroelectricity Piezoelectricity
Photogalvanics Tubes as Optical Materials
.with Na Sai Charlie Kane Petr Kral
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Carbon nanotube contacting platinum electrodes
Source
Drain
Gate
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Long wavelength physics in the extended
direction is controlled by the short
distance physics in the wrapped direction
Some examples
Semiconducting v. Conducting Carbon NTs
Pyrolectric and Piezoelectric Effects in III-Vs
(this work) Structure Specific Near
Infrared Fluorescence (in progress)
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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
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Rolling-up a graphene sheet
The (m,n) wrapping specifies a translation vector
of the graphene lattice.
mn
mod(m-n,3) 1
mod(m-n,3) 0, m?n
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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.
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Are Nanotubes Photogalvanic ?
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Heteropolar NTs 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
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Quantum Theory of Polarization (King-Smith
Vanderbilt, Phys. Rev. B47, 1651 (1993))
DP is obtained from the geometric (Berrys)
phase accumulated by the us under adiabatic
motion on a closed orbit in t-space.
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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
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The NTs electric dipole moment that depends on
its wrapping
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The magnitude of the dipole issensitive to
elastic strain (modulate d)
NTs are molecular piezoelectrics, where P is
sensitive to twist and stretch, so strain
ltgtvoltage !
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Pyroelectric v. Piezoelectric Effects
Geometrical (topological and discrete)
Strain (short range and continuously tunable)
(physics)
(chemistry)
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Piezoelectricity in a Heteropolar Sheet
elastic strain lowers the threefold symmetry of
the BN sheet producing an electric polarization
stretch
twist
3m symmetry
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Elastic Strain on a Heteropolar Tube
armchair
zigzag
stretch
twist
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Calculated (N-TB) Piezo-Response of Nanotubes
zigzag
armchair
sheets
N-TB
DFT
p electron response dominates 1/R2 finite
size corrections
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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
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Piezoelectricity of Chiral Tubes
From N-TB (calculations for (5,m) (6,m) (12,m)
families)
mapped sheet response
mapped sheet response
tube
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Size (R) Scaling of the Piezoelectric Constants
of Chiral Tubes
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Photogalvanic Effects inHeteropolar Tubes
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C, BN NTs 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)
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Physical Properties ? Control of Composition AND
Geometry
challenges
opportunities
highly ordered (coherent) structures access
to quantum geometrical effects
phenomenology systematics in families
control CG in synthesis structural
sorting assembly of networks and
superstructures
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Near-infrared Photoluminescence from Single-wall
Carbon Nanotubes
Excitation (661 nm)
Emission (? 850 nm)
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Fluorescence Spectroscopy
FS reveals electronic gap structure outside
the conventional band model.
The ratio problem Gap Ratio lt 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
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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.
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But could a flame ever burn for a match and a
stick? It did quite literally he burned up
pretty quick.
childrens poetry by Tim Burton (1997)