piezoelectric nanotubes (!) electrons on carbon nt’s heteropolar nanotubes pyroelectricity...
TRANSCRIPT
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
Source DrainGate
“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 2D..
…is replacedby an unconventional E(k) relation on thegraphene lattice
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
Backscattering from elastic strains: bend and twist
Twist (but not bend) canbackscatter electronson an armchair tube.
this is responsible forthe T-linear observered resistivity.
Are Nanotubes Photogalvanic ?
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
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.
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
The NT’s electric dipole moment that depends on its wrapping
0,3
FvR
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 !
Pyroelectric v. Piezoelectric Effects
Geometrical (topological and discrete)
Strain (short range and continuously “tunable”)
(physics) (chemistry)
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:
Elastic Strain on a Heteropolar Tube
stretch
twist
armchair zigzag
Calculated (N-TB) Piezo-Response of Nanotubes
zigzag armchair
N-TB
DFT
• electron response dominates• 1/R^2 finite size corrections
sheets
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 …
Piezoelectricity of Chiral Tubes
mapped sheet response
From N-TB (calculations for (5,m) (6,m) (12,m) families)
tube
mapped sheet response
Size (R) Scaling of the Piezoelectric Constants of Chiral Tubes
Photogalvanic Effects inHeteropolar Tubes
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)
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”
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)
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
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)