Quantum Interference in Multiwall Carbon Nanotubes

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Quantum Interference in Multiwall Carbon
Nanotubes

• Christoph Strunk

Universität Regensburg
Coworkers and Acknowledgements B. Stojetz, Ch.
Hagen, Ch. Hendlmeier (Regensburg) L. Forró, E.
Ljubovic (Lausanne) A. Bachtold , M. Buitelaar,
Ch. Schönenberger (Basel) K. Richter, G.
Cuniberti (Regensburg) R. Schäfer (Karlsruhe)
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multiwalled carbon nanotubes
S. Ijima, Nature 354, 56 (1991)
26 nm
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Outline
Introduction Electronic structure of carbon
nanotubes Quantum interference Changing the
electron density Coulomb blockade Perspectives
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Graphene a single sheet of graphite
sp2-hybridization leads to planar carbon
sheets 2D electronic bandstructure determined by
p-orbitals p-bands touch at K-points
K
K
G
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wrapping graphene to nanotubes
RA
RB
wrapping vector R determines
chirality (real space)
allowed k-vectors (k-space)
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Density of states
Metallic behavior
K
K
K
K
Semicond. behavior
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are MWNTs ballistic conductors at 300 K?
G (2e²/h)
z-position (nm)
Conductance changes in units of 2e²/h !
Frank, et al., Science 280, 1744 (1998)
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Weak localization and universal conductance
fluctuations (UCF)
signatures of coherent backscattering in
disordered quantum wires
Ai
r
r
Aj
Closed loop of time reversed paths
r r
A A-
enhanced backscattering probability!
Magnetic field breaks time-reversal
symmetry coherent backscattering suppressed by
magnetic field negative magnetoresistance near
B0 reproducible fluctuation pattern specific
for impurity configuration magneto-fingerprints

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Weak localization and universal conductance
fluctuations (UCF)
signatures of coherent backscattering in
disordered quantum wires
Ai
F
r
r
Aj
Closed loop of time reversed paths
r r
F
A A-
enhanced backscattering probability!
Magnetic field breaks time-reversal
symmetry coherent backscattering suppressed by
magnetic field negative magnetoresistance near
B0 reproducible fluctuation pattern specific
for impurity configuration magneto-fingerprints

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A. Bachtold et al., 98
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Similar results obtained by many other
groups Leuven, IBM, Stuttgart, Helsinki ..
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How to confirm the presence of elastic scattering
?
Induce drastic change of electron density by gate
electrode (distance 2-3 nm) Change number of
current carrying subbands Tune electrochemical
potential through charge neutrality point Induce
transition between quasi-1dim and strictly 1dim
transport ?
Au contact
Au contact
Doping state of MWNTs Effect on weak
localization ? Effects of Coulomb interaction ?
EF
MWNT
Al gate (native oxide)
200 nm
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Gate sweep
high temperatures shallow minimum in conductance
low temperatures universal conductance
fluctuations (UCFs) (curves shifted)
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Universal conductance fluctuations
Interference of many diffusion paths lead to
aperiodic fluctuation pattern in the conductance
lF
lF gt tube diameter (28 nm) lF lt tube length (400
nm)
Ensemble averaging of conductance fluctuations DG
if L lt lF
vary interference pattern by applying electric or
magnetic fields determine phase coherence length
lF at different temperatures
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Magnetoresistance at different gate voltages
magnetic field B perpendicular to tube
axis magnetoresistance traces taken at various
gate voltages (arrows) select different members
within statistical ensemble of magneto-fingerprint
s
T 1.7 K
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Ensemble averaging
average
weak localization peak survives averaging UCFs
averaged out partially, but not completely
Stojetz et al., New J. Phys. 04
T 1.7 K (curves shifted)
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Weak localization
conductance correction due to weak localization
1.7 K
Fitting WL-theory to data T (K) lf (nm)
1.7 150 20 80 40
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20 K
40 K
effective width Wdiameter/2 requiredorigin
flux-cancellation effects ?
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Phase coherence length
diamonds UCF measurement triangles weak
localization line prediction for
electron-electron dephasing T-1/3elastic mfp
14 nm

? UCF ? WL
Good agreement of lF from WL and
UCFs Substantiation of diffusive transport
picture Further experiments required to identify
origin of disorder
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Measure a larger statistical ensemble
shallow conductance minimum at 300K
emerging fluctuation pattern at lower T
decrease of correlation voltage Vc
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Crossover to Coulomb blockade at lowest T
decrease of average conductance
Resonant transmission of single channels?
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disordered MWNT with irregular Coulomb diamonds
typical capacitances CGate 55 aF CS
800 aF charging energyEc 100 meV 1.2 K
T30 mK
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broad zero bias anomalies remain at higher T
T 10 K
T 3 K
estimated subband spacing 25 meV gate lever arm
DEF/UGate 1/10
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Magnetoconductance shows pronounced gate
dependence
T 10 K
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Open questions
Source of disorder -extrinsic or intrinsic
? Strength of disorder? Effect of Coulomb
blockage and number of channels on the shape of
the WL-peak? Gate dependence of Aharonov-Bohm
effect in parallel magnetic field?
B