Physics of multiwalled carbon nanotubes

1D TDOS in disordered carbon nanotubes

The tunneling conductance of junctions between a highly disordered carbon nanotube and a metallic electrode shows a characteristic zero-bias anomaly due to electron-electron interactions. Due to the high resistivity of the nanotube material, around 50 kΩ/μM, the field diffusion is rather slow. In wide enough contacts, the finite size of the junctions comes into play, and the observed anomaly can be described using theoretical model for 1D tunnel junctions.

The disorder-enhanced anomaly is well known in metallic systems, where the anomaly typically is small, only a few percent. In our disordered nanotubes we observe a much larger anomaly, and this opens a possibility to study the phenomenon in non-perturbative regime. The temperature dependence of the conductivity in our samples is found to be in good agreement with recent theoretical work (Rollbühler and Grabert, PRL 87, 126804 (2001); Mischenko et al. PRL 87, 246801 (2001)). The tunneling conductance is roughly given by G ~ e-(T/T0)/2.

The disordered nanotubes are not suitable for fabrication of SET transistors, because the high resistivity of the nanotube suppresses the SET oscillations. The Coulomb blockade occurs in a single junction, isolated by the high resistance of the nanotube, irrespective of the existence of the other junction.

Quantum transport

In order to realize future nanotube electronics, it is not only necessary to thoroughly understand their transport properties, but also to be able to fabricate devices possessing the desirable qualities. While the latter goal is still distant, the transport in single-walled nanotubes is already understood quite well.

With multiwalled carbon nanotubes the situation is more complicated. Room temperature ballistic transport has been reported, but in the typical configuration with MWNTs on an insulating substrate, diffusive transport behaviour is mainly observed: interference effects are found to be significant, either in 1D or 2D depending on the electron mean free path.

We have investigated electron transport in extremely disordered MWNTs as a function of magnetic field and temperature. Our AFM studies reveal that the curvature of CVD tubes is intrinsic, and due to a high concentration of structural defects. We find that in our CVD grown tubes the electron mean free path l and phase coherence length Lφ are very short. In fact, l turns out to be so short that our nanotube samples are near the strong localization regime.

The dephasing length obtained from the above fit, and results of similar analysis for sample 12. Power law fits of Lφ∝ T-p/2 give p = 0.53 and 0.36 for samples 4 and 12, respectively. The thick solid line is the cross-over between weak and strong localization in the e-e scattering picture. The dashed line is the contribution of the 2D electron-electron scattering for sample 4 assuming D ~ 2 cm2/s.

Transmission lines

The basic charged excitations in carbon nanotubes are plasmons, in a similar fashion as in ordinary transmission lines. Owing to their small density of conduction electrons, however, carbon nanotubes display rather extraordinary line parameters.

Tunneling conductance at high voltages was used to determine the transmission-line parameters of the arc-discharge-grown multiwalled carbon nanotube samples. The fits yield a characteristic impedance of 1.3 - 7.7 kΩ and kinetic inductance of 0.1 - 4.2 nH/μm for the measured samples.

At low voltages, the tunneling conductance obeys non-Ohmic power law, which is predicted both by the Luttinger liquid and the environment-quantum-fluctuation theories. However, at higher voltages we observe a crossover to Ohm's law with a Coulomb-blockade offset, which agrees with the environmental quantum-fluctuation theory, but cannot be explained by the Luttinger-liquid theory.

High voltage IV -curves (both positive and negative polarities) on a log-log plot for four samples T1-T4. The dashed line illustrates linear behavior. Our data are rather close to a single power law with small exponent but, at larger values of voltage, there is gradual tendency toward a linear law as expected for a single junction in a resistive environment.

Related publications

  • Low-frequency current noise and resistance fluctuations in multiwalled carbon nanotubes

R. Tarkiainen, L. Roschier, M. Ahlskog, M.A. Paalanen, and P.J. Hakonen

Physica E 28, 57 (2005)

  • Tunneling spectroscopy of disordered multiwalled carbon nanotubes

R. Tarkiainen, M. Ahlskog, M.A. Paalanen, A. Zyuzin, P.J. Hakonen

Phys. Rev. B 71, 125425 (2005)

  • Transport in strongly disordered multiwalled carbon nanotubes

R. Tarkiainen, M. Ahlskog, A. Zyuzin, P.J. Hakonen, and M.A. Paalanen

Phys. Rev. B 69, 033402 (2004)

  • Transport in disordered carbon nanotubes

R. Tarkiainen, M. Ahlskog, P.J. Hakonen, and M.A. Paalanen

Physica E 18, 206 (2003)

  • Multiwalled carbon nanotube: Luttinger versus Fermi liquid

R. Tarkiainen R, M. Ahlskog, J.S. Penttilä, L. Roschier, P.J. Hakonen, M.A. Paalanen, and E.B. Sonin

Phys. Rev. B 64, 195412 (2001)