When electrons pass through a cylindrical electrical conductor aligned in a magnetic ®eld, their wave-like nature manifests itself as a periodic oscillation in the electrical resistance as a function of the enclosed magnetic¯ux 1 . This phenomenon re¯ects the dependence of the phase of the electron wave on the magnetic ®eld, known as the Aharonov±Bohm effect 2 , which causes a phase difference, and hence interference, between partial waves encircling the conductor in opposite directions. Such oscillations have been observed in micrometre-sized thin-walled metallic cylinders 3±5 and lithographically fabricated rings 6±8 . Carbon nanotubes 9,10 are composed of individual graphene sheets rolled into seamless hollow cylinders with diameters ranging from 1 nm to about 20 nm. They are able to act as conducting molecular wires 11±18 , making them ideally suited for the investigation of quantum interference at the single-molecule level caused by the Aharonov±Bohm effect. Here we report magnetoresistance measurements on individual multi-walled nanotubes, which display pronounced resistance oscillations as a function of magnetic ux. We ®nd that the oscillations are in good agreement with theoretical predictions for the Aharonov±Bohm effect in a hollow conductor with a diameter equal to that of the outermost shell of the nanotubes. In some nanotubes we also observe shorter-period oscillations, which might result from anisotropic electron currents caused by defects in the nanotube lattice.In a diffusive and thin-walled metallic cylinder, a prominent periodic quantum correction to the resistance arises from the interference of closed electron trajectories that encircle the cylinder once. The phase difference Df between each such trajectory ¡ and the time-reversed counter-propagating trajectory ¡9 (Fig. 1a) is solely determined by the magnetic¯ux © enclosed: Df 2p2e=h©, where e and h are the electron charge and Planck's constant, respectively. Consequently, the electrical resistance has an oscillating contribution with period h/2e, known as the Altshuler± Aronov±Spivak (AAS) effect 1 . For zero magnetic¯ux, these interference terms add up constructively, increasing electron backscattering and thereby the electrical resistance, an effect known as weak localization 19 . For a thin metallic ®lm in a perpendicular magnetic ®eld, the weak-localization resistance correction monotonically disappears in higher ®elds (negative magnetoresistance, MR). In contrast, for a cylinder in a parallel magnetic ®eld, weak localization is periodically modulated with a magnetic-®eld period given by DB h=2e=r 2 p, where r is the radius of the cylinder.We have carried out electric-transport measurements on multiwalled carbon nanotubes (MWNTs) composed of multiple coaxial graphene cylinders, in a magnetic ®eld parallel to the axis of the nanotubes. An example is shown in Fig. 1b. Coulomb blockade can strongly affect electrical transport in small structures, and we therefore use samples containing only a single contacted nanotube with low contact resis...

Coulomb interaction effects have pronounced consequences in carbon nanotubes due to their 1D nature. In particular, correlations imply the breakdown of Fermi liquid theory and typically lead to Luttinger liquid behavior characterized by pronounced power-law suppression of the transport current and the density of states, and spin-charge separation. This paper provides a review of the current understanding of non-Fermi liquid effects in metallic single-wall nanotubes (SWNTs). We provide a self-contained theoretical discussion of electron-electron interaction effects and show that the tunneling density of states exhibits power-law behavior. The power-law exponent depends on the interaction strength parameter g and on the geometry of the setup. We then show that these features are observed experimentally by measuring the tunneling conductance of SWNTs as a function of temperature and voltage. These tunneling experiments are obtained by contacting metallic SWNTs to two nanofabricated gold electrodes. Electrostatic force microscopy (EFM) measurements show that the measured resistance is due to the contact resistance from the transport barrier formed at the electrode/nanotube junction. These EFM measurements show also the ballistic nature of transport in these SWNTs. While charge transport can be nicely attributed to Luttinger liquid behavior, spin-charge separation has not been observed so far. We briefly describe a transport experiment that could provide direct evidence for spin-charge separation.

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Gold-platinum catalytic pumps immersed in a chemical fuel are used to manipulate silica colloids. The manipulation relies on the electric field and the fluid flow generated by the pump. Catalytic pumps perform various tasks, such as the repulsion of colloids, the attraction of colloids, and the guided crystallization of colloids. We demonstrate that catalytic pumps can execute these tasks sequentially over time. Switching from one task to the next is related to the local change of the proton concentration, which modifies the colloid zeta potential and consequently the electric force acting on the colloids.

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