Amir Yacoby

Observation of electron–hole puddles in graphene using a scanning single-electron transistor

The electronic structure of graphene causes its charge carriers to behave like relativistic particles. For a perfect graphene sheet free from impurities and disorder, the Fermi energy lies at the so-called ‘Dirac point’, where the density of electronic states vanishes. But in the inevitable presence of disorder, theory predicts that equally probable regions of electron-rich and hole-rich puddles will arise. These puddles could explain graphene’s anomalous non-zero minimal conductivity at zero average carrier density. Here, we use a scanning single-electron transistor to map the local density of states and the carrier density landscape in the vicinity of the neutrality point. Our results confirm the existence of electron–hole puddles, and rule out extrinsic substrate effects as explanations for their emergence and topology. Moreover, we find that, unlike non-relativistic particles the density of states can be quantitatively accounted for by considering non-interacting electrons and holes.

Nanoscale magnetic sensing with an individual electronic spin in diamond

Detection of weak magnetic fields with nanoscale spatial resolution is an outstanding problem in the biological and physical sciences. For example, at a distance of 10 nm, the spin of a single electron produces a magnetic field of about 1 μT, and the corresponding field from a single proton is a few nanoteslas. A sensor able to detect such magnetic fields with nanometre spatial resolution would enable powerful applications, ranging from the detection of magnetic resonance signals from individual electron or nuclear spins in complex biological molecules to readout of classical or quantum bits of information encoded in an electron or nuclear spin memory. Here we experimentally demonstrate an approach to such nanoscale magnetic sensing, using coherent manipulation of an individual electronic spin qubit associated with a nitrogen-vacancy impurity in diamond at room temperature. Using an ultra-pure diamond sample, we achieve detection of 3 nT magnetic fields at kilohertz frequencies after 100 s of averaging. In addition, we demonstrate a sensitivity of 0.5 μT Hz-1/2 for a diamond nanocrystal with a diameter of 30 nm.

High-sensitivity diamond magnetometer with nanoscale resolution

Impurity centres in diamond have recently attracted attention in the context of quantum information processing. Now their use as magnetic-field sensors is explored, promising a fresh approach to single-spin detection and magnetic-field imaging at the nanoscale.

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.

Charge Fractionalization in Quantum Wires

One-dimensional metals, such as quantum wires or carbon nanotubes, can carry charge in arbitrary units, smaller or larger than a single electron charge. However, according to Luttinger theory, which describes the low-energy excitations of such systems, when a single electron is injected by tunneling into the middle of such a wire, it will tend to break up into separate charge pulses, moving in opposite directions, which carry definite fractions f and (1−f) of the electron charge, determined by a parameter g that measures the strength of charge interactions in the wire. (The injected electron will also produce a spin excitation, which will travel at a different velocity than the charge excitations.) Observing charge fractionalization physics in an experiment is a challenge in those (nonchiral) low-dimensional systems which are adiabatically coupled to Fermi liquid leads. We theoretically discuss a first important step towards the observation of charge fractionalization in quantum wires based on momentum-resolved tunneling and multi-terminal geometries, and explain the recent experimental results of H. Steinberg et al., Nature Physics 4, 116 (2008).

Measurement of the conductance of single conjugated molecules

Electrical conduction through molecules depends critically on the delocalization of the molecular electronic orbitals and their connection to the metallic contacts. Thiolated (- SH) conjugated organic molecules are therefore considered good candidates for molecular conductors: in such molecules, the orbitals are delocalized throughout the molecular backbone, with substantial weight on the sulphur–metal bonds. However, their relatively small size, typically ∼1 nm, calls for innovative approaches to realize a functioning single-molecule device. Here we report an approach for contacting a single molecule, and use it to study the effect of localizing groups within a conjugated molecule on the electrical conduction. Our method is based on synthesizing a dimer structure, consisting of two colloidal gold particles connected by a dithiolated short organic molecule, and electrostatically trapping it between two metal electrodes. We study the electrical conduction through three short organic molecules: 4,4′-biphenyldithiol (BPD), a fully conjugated molecule; bis-(4-mercaptophenyl)-ether (BPE), in which the conjugation is broken at the centre by an oxygen atom; and 1,4-benzenedimethanethiol (BDMT), in which the conjugation is broken near the contacts by a methylene group. We find that the oxygen in BPE and the methylene groups in BDMT both suppress the electrical conduction relative to that in BPD.

A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres

Controllable atomic-scale quantum systems hold great potential as sensitive tools for nanoscale imaging and metrology [1–6]. Possible applications range from nanoscale electric [7] and magnetic field sensing [4–6, 8] to single photon microscopy [1, 2], quantum information processing [9], and bioimaging [10]. At the heart of such schemes is the ability to scan and accurately position a robust sensor within a few nanometers of a sample of interest, while preserving the sensor’s quantum coherence and readout fidelity. These combined requirements remain a challenge for all existing approaches that rely on direct grafting of individual solid state quantum systems [4, 11, 12] or single molecules [2] onto scanning-probe tips. Here, we demonstrate the fabrication and room temperature operation of a robust and isolated atomic-scale quantum sensor for scanning probe microscopy. Specifically, we employ a high-purity, single-crystalline diamond nanopillar probe containing a single Nitrogen-Vacancy (NV) color center. We illustrate the versatility and performance of our scanning NV sensor by conducting quantitative nanoscale magnetic field imaging and near-field single-photon fluorescence quenching microscopy. In both cases, we obtain imaging resolution in the range of 20 nm and sensitivity unprecedented in scanning quantum probe microscopy.

Optical magnetic imaging of living cells

Magnetic imaging is a powerful tool for probing biological and physical systems. However, existing techniques either have poor spatial resolution compared to optical microscopy and are hence not generally applicable to imaging of sub-cellular structure (for example, magnetic resonance imaging), or entail operating conditions that preclude application to living biological samples while providing submicrometre resolution (for example, scanning superconducting quantum interference device microscopy, electron holography and magnetic resonance force microscopy). Here we demonstrate magnetic imaging of living cells (magnetotactic bacteria) under ambient laboratory conditions and with sub-cellular spatial resolution (400 nanometres), using an optically detected magnetic field imaging array consisting of a nanometre-scale layer of nitrogen–vacancy colour centres implanted at the surface of a diamond chip. With the bacteria placed on the diamond surface, we optically probe the nitrogen–vacancy quantum spin states and rapidly reconstruct images of the vector components of the magnetic field created by chains of magnetic nanoparticles (magnetosomes) produced in the bacteria. We also spatially correlate these magnetic field maps with optical images acquired in the same apparatus. Wide-field microscopy allows parallel optical and magnetic imaging of multiple cells in a population with submicrometre resolution and a field of view in excess of 100 micrometres. Scanning electron microscope images of the bacteria confirm that the correlated optical and magnetic images can be used to locate and characterize the magnetosomes in each bacterium. Our results provide a new capability for imaging bio-magnetic structures in living cells under ambient conditions with high spatial resolution, and will enable the mapping of a wide range of magnetic signals within cells and cellular networks.

Triplet-singlet spin relaxation via nuclei in a double quantum dot

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation; spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing.

Demonstration of entanglement of electrostatically coupled singlet-triplet qubits.

Entangling Qubits The basic building block of a quantum computer, a qubit, has been realized in many physical settings, each of which has its advantages and drawbacks. Solid-state spin qubits interact weakly with their environment and each other, leading not only to long coherence times but also to difficulties in performing multiqubit operations. Shulman et al. (p. 202) used a double quantum dot to produce a singlet-triplet qubit, where the two quantum states available are a singlet and a triplet formed by two spin-1/2 electrons. Two such qubits are then entangled by electrical gating, which affects the charge configuration of one qubit and that, in turn, influences the electric field experienced by the other. This type of two-qubit entanglement is essential for further development of quantum computing in these systems. The states of two qubits residing in a pair of double quantum dots are rendered interdependent through electrical gating. Quantum computers have the potential to solve certain problems faster than classical computers. To exploit their power, it is necessary to perform interqubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor because of their potential for scalability and miniaturization. However, their weak interactions with the environment, which lead to their long coherence times, make interqubit operations challenging. We performed a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography, we measured the full density matrix of the system and determined the concurrence and the fidelity of the generated state, providing proof of entanglement.