Marc Bockrath

Kondo resonance in a single-molecule transistor

When an individual molecule, nanocrystal, nanotube or lithographically defined quantum dot is attached to metallic electrodes via tunnel barriers, electron transport is dominated by single-electron charging and energy-level quantization. As the coupling to the electrodes increases, higher-order tunnelling and correlated electron motion give rise to new phenomena, including the Kondo resonance. To date, all of the studies of Kondo phenomena in quantum dots have been performed on systems where precise control over the spin degrees of freedom is difficult. Molecules incorporating transition-metal atoms provide powerful new systems in this regard, because the spin and orbital degrees of freedom can be controlled through well-defined chemistry. Here we report the observation of the Kondo effect in single-molecule transistors, where an individual divanadium molecule serves as a spin impurity. We find that the Kondo resonance can be tuned reversibly using the gate voltage to alter the charge and spin state of the molecule. The resonance persists at temperatures up to 30 K and when the energy separation between the molecular state and the Fermi level of the metal exceeds 100 meV.

Luttinger-liquid behaviour in carbon nanotubes

Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that the energy states of the electrons near the Fermi level EF are not qualitatively altered by Coulomb interactions. In one-dimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system, known as a Luttinger liquid, is predicted to be distinctly different from its two- and three-dimensional counterparts. For example, tunnelling into a Luttinger liquid at energies near the Fermi level is predicted to be strongly suppressed, unlike in two- and three-dimensional metals. Experiments on one-dimensional semiconductor wires, have been interpreted by using Luttinger-liquid theory, but an unequivocal verification of the theoretical predictions has not yet been obtained. Similarly, the edge excitations seen in fractional quantum Hall conductors are consistent with Luttinger-liquid behaviour, , but recent experiments failed to confirm the predicted relationship between the electrical properties of the bulk state and those of the edge states. Electrically conducting single-walled carbon nanotubes (SWNTs) represent quantum wires that may exhibit Luttinger-liquid behaviour, . Here we present measurements of the conductance of bundles (‘ropes’) of SWNTs as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid. In particular, we find that the conductance and differential conductance scale as power laws with respect to temperature and bias voltage, respectively, and that the functional forms and the exponents are in good agreement with theoretical predictions.

Electron liquids and solids in one dimension

Even though bulk metallic systems contain a very large number of strongly interacting electrons, their properties are well described within Landaus Fermi liquid theory of non-interacting quasiparticles. Although many higher-dimensional systems can be successfully understood on the basis of such non-interacting theories, this is not possible for one-dimensional systems. When confined to narrow channels, electron interaction gives rise to such exotic phenomena as spin–charge separation and the emergence of correlated-electron insulators. Such strongly correlated electronic behaviour has recently been seen in experiments on one-dimensional carbon nanotubes and nanowires, and this behaviour challenges the theoretical description of such systems.

Fabry-Perot interference in a nanotube electron waveguide

The behaviour of traditional electronic devices can be understood in terms of the classical diffusive motion of electrons. As the size of a device becomes comparable to the electron coherence length, however, quantum interference between electron waves becomes increasingly important, leading to dramatic changes in device properties. This classical-to-quantum transition in device behaviour suggests the possibility for nanometer-sized electronic elements that make use of quantum coherence. Molecular electronic devices are promising candidates for realizing such device elements because the electronic motion in molecules is inherently quantum mechanical and it can be modified by well defined chemistry. Here we describe an example of a coherent molecular electronic device whose behaviour is explicitly dependent on quantum interference between propagating electron waves—a Fabry–Perot electron resonator based on individual single-walled carbon nanotubes with near-perfect ohmic contacts to electrodes. In these devices, the nanotubes act as coherent electron waveguides, with the resonant cavity formed between the two nanotube–electrode interfaces. We use a theoretical model based on the multichannel Landauer–Büttiker formalism to analyse the device characteristics and find that coupling between the two propagating modes of the nanotubes caused by electron scattering at the nanotube–electrode interfaces is important.

Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators

Ultraminiaturized mass spectrometers are highly sought-after tools, with numerous applications in areas such as environmental protection, exploration, and drug development. We realize atomic scale mass sensing using doubly clamped suspended carbon nanotube nanomechanical resonators, in which their single-electron transistor properties allows self-detection of the nanotube vibration. We use the detection of shifts in the resonance frequency of the nanotubes to sense and determine the inertial mass of atoms as well as the mass of the nanotube. This highly sensitive mass detection capability may eventually enable applications such as on-chip detection, analysis, and identification of compounds.

Disorder, Pseudospins, and Backscattering in Carbon Nanotubes

We address the effects of disorder on the conducting properties of metal and semiconducting carbon nanotubes. Experimentally, the mean free path is found to be much larger in metallic tubes than in doped semiconducting tubes. We show that this result can be understood theoretically if the disorder potential is long ranged. The effects of a pseudospin index that describes the internal sublattice structure of the states lead to a suppression of scattering in metallic tubes, but not in semiconducting tubes. This conclusion is supported by tight-binding calculations.

Graphene-based atomic-scale switches.

Graphenes remarkable mechanical and electrical properties, combined with its compatibility with existing planar silicon-based technology, make it an attractive material for novel computing devices. We report the development of a nonvolatile memory element based on graphene break junctions. Our devices have demonstrated thousands of writing cycles and long retention times. We propose a model for device operation based on the formation and breaking of carbon atomic chains that bridge the junctions. We demonstrate information storage based on the concept of rank coding, in which information is stored in the relative conductance of graphene switches in a memory cell.

Stacking-dependent band gap and quantum transport in trilayer graphene

Graphene is an extraordinary two-dimensional (2D) system with chiral charge carriers and fascinating electronic, mechanical and thermal properties. In multilayer graphene, stacking order provides an important yet rarely explored degree of freedom for tuning its electronic properties. For instance, Bernal-stacked trilayer graphene (B-TLG) is semi-metallic with a tunable band overlap, and rhombohedral-stacked trilayer graphene (r-TLG) is predicted to be semiconducting with a tunable band gap. These multilayer graphenes are also expected to exhibit rich novel phenomena at low charge densities owing to enhanced electronic interactions and competing symmetries. Here we demonstrate the dramatically different transport properties in TLG with different stacking orders, and the unexpected spontaneous gap opening in charge neutral r-TLG. At the Dirac point, B-TLG remains metallic, whereas r-TLG becomes insulating with an intrinsic interaction-driven gap ~6 meV. In magnetic fields, well-developed quantum Hall (QH) plateaux in r-TLG split into three branches at higher fields. Such splitting is a signature of the Lifshitz transition, a topological change in the Fermi surface, that is found only in r-TLG. Our results underscore the rich interaction-induced phenomena in trilayer graphene with different stacking orders, and its potential towards electronic applications.

Quantum Phase Slips in Superconducting Nanowires

We have measured the resistance vs temperature of more than 20 superconducting nanowires with nominal widths ranging from 10 to 22 nm and lengths from 100 nm to 1 microm. With decreasing cross-sectional areas, the wires display increasingly broad resistive transitions. The data are in very good agreement with a model that includes both thermally activated phase slips close to T(c) and quantum phase slips (QPS) at low temperatures, but disagree with an earlier model based on a critical value of R(N)/R(q). Our measurements provide strong evidence for QPS in thin superconducting wires.

Spin splitting and even-odd effects in carbon nanotubes

The level spectrum of a single-walled carbon nanotube rope, studied by transport spectroscopy, shows Zeeman splitting in a magnetic field parallel to the tube axis. The pattern of splittings implies that the spin of the ground state alternates by 1/2 as consecutive electrons are added. Other aspects of the Coulomb blockade characteristics, including the current-voltage traces and peak heights, also show corresponding even-odd effects.