Shaping Electron Wave Functions in a Carbon Nanotube with a Parallel Magnetic Field.

A magnetic field, through its vector potential, usually causes measurable changes in the electron wave function only in the direction transverse to the field. Here, we demonstrate experimentally and theoretically that, in carbon nanotube quantum dots combining cylindrical topology and bipartite hexagonal lattice, a magnetic field along the nanotube axis impacts also the longitudinal profile of the electronic states. With the high (up to 17 T) magnetic fields in our experiment, the wave functions can be tuned all the way from a "half-wave resonator" shape with nodes at both ends to a "quarter-wave resonator" shape with an antinode at one end. This in turn causes a distinct dependence of the conductance on the magnetic field. Our results demonstrate a new strategy for the control of wave functions using magnetic fields in quantum systems with a nontrivial lattice and topology.

Nanomechanical Characterization of the Kondo Charge Dynamics in a Carbon Nanotube.

Using the transversal vibration resonance of a suspended carbon nanotube as a charge detector for its embedded quantum dot, we investigate the case of strong Kondo correlations between a quantum dot and its leads. We demonstrate that even when large Kondo conductance is carried at odd electron number, the charging behavior remains similar between odd and even quantum dot occupations. While the Kondo conductance is caused by higher order processes, a sequential tunneling only model can describe the time-averaged charge. The gate potentials of the maximum current and fastest charge increase display a characteristic relative shift, which is suppressed at increased temperature. These observations agree very well with models for Kondo-correlated quantum dots.

Secondary Electron Interference from Trigonal Warping in Clean Carbon Nanotubes.

We investigate Fabry-Perot interference in an ultraclean carbon nanotube resonator. The conductance shows a clear superstructure superimposed onto conventional Fabry-Perot oscillations. A sliding average over the fast oscillations reveals a characteristic slow modulation of the conductance as a function of the gate voltage. We identify the origin of this secondary interference in intervalley and intravalley backscattering processes which involve wave vectors of different magnitude, reflecting the trigonal warping of the Dirac cones. As a consequence, the analysis of the secondary interference pattern allows us to estimate the chiral angle of the carbon nanotube.

Co-sputtered MoRe thin films for carbon nanotube growth-compatible superconducting coplanar resonators.

Molybdenum rhenium alloy thin films can exhibit superconductivity up to critical temperatures of T(c)=15K. At the same time, the films are highly stable in the high-temperature methane/hydrogen atmosphere typically required to grow single wall carbon nanotubes. We characterize molybdenum rhenium alloy films deposited via simultaneous sputtering from two sources, with respect to their composition as function of sputter parameters and their electronic dc as well as GHz properties at low temperature. Specific emphasis is placed on the effect of the carbon nanotube growth conditions on the film. Superconducting coplanar waveguide resonators are defined lithographically; we demonstrate that the resonators remain functional when undergoing nanotube growth conditions, and characterize their properties as function of temperature. This paves the way for ultra-clean nanotube devices grown in situ onto superconducting coplanar waveguide circuit elements.

Universality of the Kondo effect in quantum dots with ferromagnetic leads.

We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. Most of the Kondo resonances exhibit a splitting, which depends on the tunnel coupling to the leads and an external magnetic field B, but only weakly on the gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on gµ(B)(B-B(c))/k(B)T(K), where T(K) is the Kondo temperature and B(c) the external field compensating the splitting.

Pumping of vibrational excitations in the coulomb-blockade regime in a suspended carbon nanotube.

Low-temperature transport spectroscopy measurements on a suspended few-hole carbon nanotube quantum dot are presented, showing a gate-dependent harmonic excitation spectrum which, strikingly, occurs in the Coulomb-blockade regime. The quantized excitation energy corresponds to the scale expected for longitudinal vibrations of the nanotube. The electronic transport processes are identified as cotunnel-assisted sequential tunneling, resulting from nonequilibrium occupation of the mechanical mode. They appear only above a high-bias threshold at the scale of electronic nanotube excitations. We discuss models for the pumping process that explain the enhancement of the nonequilibrium occupation and show that it is connected to a subtle interplay between electronic and vibrational degrees of freedom.

Strong coupling between single-electron tunneling and nanomechanical motion.

Nanoscale resonators that oscillate at high frequencies are useful in many measurement applications. We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 10(5) allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Additional evidence for the strong coupling of mechanical motion and electron tunneling is provided by an energy transfer to the electrons causing mechanical damping and unusual nonlinear behavior. We also discovered that a direct current through the nanotube spontaneously drives the mechanical resonator, exerting a force that is coherent with the high-frequency resonant mechanical motion.