piezoelectric nanotubes (!) electrons on carbon nt’s heteropolar nanotubes pyroelectricity...
TRANSCRIPT
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Piezoelectric Nanotubes (!)
• Electrons on Carbon NT’s
• 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 DrainGate
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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 NT’s
• Pyrolectric and Piezoelectric Effects in III-V’s (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 replacedby an unconventional E(k) relation on thegraphene lattice
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The (m,n) wrapping specifies a translation vector of the graphene lattice.
Rolling-up a graphene sheet
m=n mod(m-n,3) = ±1 mod(m-n,3) = 0, mn
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Backscattering from elastic strains: bend and twist
Twist (but not bend) canbackscatter electronson an armchair tube.
this is responsible forthe T-linear observered resistivity.
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Are Nanotubes Photogalvanic ?
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Heteropolar NT’s of Boron Nitride
BN is the III-V homologto 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))
0 ( )HH H t
10
P PP dt dt
( )| ( ) ( , )2ieP d u u k
P is obtained from the geometric (Berry’s) phaseaccumulated by the u’s under adiabatic motion on a closed orbit in -space.
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Nanotube Polarization as a Geometric Phase
† ( )( , , )
( )xFx
xF
v q iH q
v q i
Control parameters: qx, ,
with valence eigenstates that adiabatically follow
ˆexp( )2
v i 2 2 2
( )
2 ( )xx jF
j F
e ev p v e v
v q
sum over states and integrate over to obtain
2 2 2arctan( )x
se Wps W
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The NT’s electric dipole moment that depends on its wrapping
0,3
FvR
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The magnitude of the dipole issensitive to elastic strain (modulate
)
NT’s are molecular piezoelectrics, where P is sensitive to twist and stretch, so strain <=>voltage !
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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 sheetproducing an electric polarization
stretch twist
xxxxxx
Pe
xxx xyy yxy yyxe e e e
yyxy
xy
Pe
3m symmetry:
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Elastic Strain on a Heteropolar Tube
stretch
twist
armchair zigzag
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Calculated (N-TB) Piezo-Response of Nanotubes
zigzag armchair
N-TB
DFT
• electron response dominates• 1/R^2 finite size corrections
sheets
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Chiral Tubes
• Chiral tubes have a wrapping vector high symmetry translation of the BN sheet (chiral angle ).
( ) ( ) ( )iaijk jb kc abcabc
e R R R e
11 sin(3 ) xxxe e 14 cos(3 ) yxye e stretch twist
• Electric Dipole couples to both stretch and torsion bilinear stretch-twist coupling!
• Low Symmetry Large Unit Cell, but …
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Piezoelectricity of Chiral Tubes
mapped sheet response
From N-TB (calculations for (5,m) (6,m) (12,m) families)
tube
mapped sheet response
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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 NT’s are prototypes with many other compact meso-phases formed by folding lamellae
MoS2
Remska et al. Science 292, 479 (2001)
WS2
Single- anddouble- 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)
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Physical Properties Control ofComposition AND Geometry
challenges opportunities
• 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”
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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 < 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 RangeInteraction
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.
children’s poetry by Tim Burton (1997)