Showing papers on "Electron published in 2006"

Detection of Individual Gas Molecules Absorbed on Graphene

Abstract: The ultimate aspiration of any detection method is to achieve such a level of sensitivity that individual quanta of a measured value can be resolved. In the case of chemical sensors, the quantum is one atom or molecule. Such resolution has so far been beyond the reach of any detection technique, including solid-state gas sensors hailed for their exceptional sensitivity. The fundamental reason limiting the resolution of such sensors is fluctuations due to thermal motion of charges and defects which lead to intrinsic noise exceeding the sought-after signal from individual molecules, usually by many orders of magnitude. Here we show that micrometre-size sensors made from graphene are capable of detecting individual events when a gas molecule attaches to or detaches from graphenes surface. The adsorbed molecules change the local carrier concentration in graphene one by one electron, which leads to step-like changes in resistance. The achieved sensitivity is due to the fact that graphene is an exceptionally low-noise material electronically, which makes it a promising candidate not only for chemical detectors but also for other applications where local probes sensitive to external charge, magnetic field or mechanical strain are required.

Chiral tunnelling and the Klein paradox in graphene

Abstract: The so-called Klein paradox—unimpeded penetration of relativistic particles through high and wide potential barriers—is one of the most exotic and counterintuitive consequences of quantum electrodynamics. The phenomenon is discussed in many contexts in particle, nuclear and astro-physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment using electrostatic barriers in single- and bi-layer graphene. Owing to the chiral nature of their quasiparticles, quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, non-relativistic electrons. Massless Dirac fermions in graphene allow a close realization of Klein’s gedanken experiment, whereas massive chiral fermions in bilayer graphene offer an interesting complementary system that elucidates the basic physics involved.

Electronic structure calculations with dynamical mean-field theory

Abstract: We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly{correlated materials where the one{electron description breaks down. We illustrate the method with several examples where interactions play a dominant role: systems near metal{insulator transition, systems near volume collapse transition, and systems with local moments.

GeV electron beams from a centimetre-scale accelerator

Abstract: Gigaelectron volt (GeV) electron accelerators are essential to synchrotron radiation facilities and free-electron lasers, and as modules for high-energy particle physics. Radiofrequency-based accelerators are limited to relatively low accelerating fields (10–50 MV m−1), requiring tens to hundreds of metres to reach the multi-GeV beam energies needed to drive radiation sources, and many kilometres to generate particle energies of interest to high-energy physics. Laser-wakefield accelerators1,2 produce electric fields of the order 10–100 GV m−1 enabling compact devices. Previously, the required laser intensity was not maintained over the distance needed to reach GeV energies, and hence acceleration was limited to the 100 MeV scale3,4,5. Contrary to predictions that petawatt-class lasers would be needed to reach GeV energies6,7, here we demonstrate production of a high-quality electron beam with 1 GeV energy by channelling a 40 TW peak-power laser pulse in a 3.3-cm-long gas-filled capillary discharge waveguide8,9.

Optics in the relativistic regime

Abstract: The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

Tunable Quasi-Two-Dimensional Electron Gases in Oxide Heterostructures

Abstract: We report on a large electric-field response of quasi-two-dimensional electron gases generated at interfaces in epitaxial heterostructures grown from insulating oxides. These device structures are characterized by doping layers that are spatially separated from high-mobility quasi-two-dimensional electron gases and therefore present an oxide analog to semiconducting high-electron mobility transistors. By applying a gate voltage, the conductivity of the electron gases can be modulated through a quantum phase transition from an insulating to a metallic state.

Electron acceleration from contracting magnetic islands during reconnection

Abstract: Electrons gain kinetic energy by reflecting from the ends of the contracting 'magnetic islands' that form as reconnection proceeds. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. A long-standing problem in the study of space and astrophysical plasmas is to explain the production of energetic electrons as magnetic fields ‘reconnect’ and release energy. In the Earth's magnetosphere, electron energies reach hundreds of thousands of electron volts (refs 1–3), whereas the typical electron energies associated with large-scale reconnection-driven flows are just a few electron volts. Recent observations further suggest that these energetic particles are produced in the region where the magnetic field reconnects4. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons5,6. Here we show that electrons gain kinetic energy by reflecting from the ends of the contracting ‘magnetic islands’ that form as reconnection proceeds. The mechanism is analogous to the increase of energy of a ball reflecting between two converging walls—the ball gains energy with each bounce. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. The back pressure of the energetic electrons throttles reconnection so that the electron energy gain is a large fraction of the released magnetic energy. The resultant energy spectra of electrons take the form of power laws with spectral indices that match the magnetospheric observations.

Single defect centres in diamond: A review

Abstract: The nitrogen vacancy and some nickel related defects in diamond can be observed as single quantum systems in diamond by their fluorescence. The fabrication of single colour centres occurs via generation of vacancies or via controlled nitrogen implantation in the case of the nitrogen vacancy (NV) centre. The NV centre shows an electron paramagnetic ground and optically excited state. As a result electron and nuclear magnetic resonance can be carried out on single defects. Due to the localized nature of the electron spin wavefunction hyperfine coupling to nuclei more than one lattice constant away from the defect as dominated by dipolar interaction. As a consequence the coupling to close nuclei leads to a splitting in the spectrum which allows for optically detected electron nuclear double resonance. The contribution discusses the physics of the NV and other defect centre from the perspective of single defect centre spectroscopy.

Controlled injection and acceleration of electrons in plasma wakefields by colliding laser pulses

Abstract: In laser-plasma-based accelerators, an intense laser pulse drives a large electric field (the wakefield) which accelerates particles to high energies in distances much shorter than in conventional accelerators. These high acceleration gradients, of a few hundreds of gigavolts per metre, hold the promise of compact high-energy particle accelerators. Recently, several experiments have shown that laser-plasma accelerators can produce high-quality electron beams, with quasi-monoenergetic energy distributions at the 100 MeV level. However, these beams do not have the stability and reproducibility that are required for applications. This is because the mechanism responsible for injecting electrons into the wakefield is based on highly nonlinear phenomena, and is therefore hard to control. Here we demonstrate that the injection and subsequent acceleration of electrons can be controlled by using a second laser pulse. The collision of the two laser pulses provides a pre-acceleration stage which provokes the injection of electrons into the wakefield. The experimental results show that the electron beams obtained in this manner are collimated (5 mrad divergence), monoenergetic (with energy spread <10 per cent), tuneable (between 15 and 250 MeV) and, most importantly, stable. In addition, the experimental observations are compatible with electron bunch durations shorter than 10 fs. We anticipate that this stable and compact electron source will have a strong impact on applications requiring short bunches, such as the femtolysis of water, or high stability, such as radiotherapy with high-energy electrons or radiography for materials science.

Sub-Poissonian Shot Noise in Graphene

Abstract: We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length $L$, width $W$, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order ${e}^{2}/h$ at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals $1/3$, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.

Many-electron self-interaction error in approximate density functionals.

Abstract: One of the most important challenges in density functional theory (DFT) is the proper description of fractional charge systems relating to the self-interaction error (SIE). Traditionally, the SIE has been formulated as a one-electron problem, which has been addressed in several recent functionals. However, these recent one-electron SIE-free functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the many-electron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from many-electron SIE. Finally, we give a SIE classification of density functionals.

Control of Electron Localization in Molecular Dissociation

Abstract: We demonstrated how the subcycle evolution of the electric field of light can be used to control the motion of bound electrons. Results are presented for the dissociative ionization of deuterium molecules (D2 ⇒ D+ + D), where asymmetric ejection of the ionic fragment reveals that light-driven intramolecular electronic motion before dissociation localizes the electron on one of the two D+ ions in a controlled way. The results extend subfemtosecond electron control to molecules and provide evidence of its usefulness in controlling reaction dynamics.

Room-temperature miscibility gap in LixFePO4.

Abstract: The rechargeable lithium-ion cell is an advanced energy-storage system. However, high cost, safety hazards, and chemical instability prohibit its use in large-scale applications. An alternative cathode material, LiFePO4, solves these problems, but has a kinetic problem involving strong electron/hole localization1. One reason for this is believed to be the limited carrier density in the fixed monovalent Fe3+PO4/LiFe2+PO4 two-phase electrode reaction in LixFePO4. Here, we provide experimental evidence that LixFePO4, at room temperature, can be described as a mixture of the Fe3+/Fe2+ mixed-valent intermediate LiαFePO4 and Li1−βFePO4 phases. Using powder neutron diffraction, the site occupancy numbers for lithium in each phase were refined to be α=0.05 and 1−β=0.89. The corresponding solid solution ranges outside the miscibility gap (0

Quantum spin-Hall effect and topologically invariant Chern numbers.

Abstract: We present a topological description of the quantum spin-Hall effect (QSHE) in a two-dimensional electron system on a honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlin gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states and determine a phase diagram for the QSHE.

Nonlinear theory for relativistic plasma wakefields in the blowout regime.

Abstract: We present a theory for nonlinear, multidimensional plasma waves with phase velocities near the speed of light. It is appropriate for describing plasma waves excited when all electrons are expelled out from a finite region by either the space charge of a short electron beam or the radiation pressure of a short intense laser. It works very well for the first bucket before phase mixing occurs. We separate the plasma response into a cavity or blowout region void of all electrons and a sheath of electrons just beyond the cavity. This simple model permits the derivation of a single equation for the boundary of the cavity. It works particularly well for narrow electron bunches and for short lasers with spot sizes matched to the radius of the cavity. It is also used to describe the structure of both the accelerating and focusing fields in the wake.

Conduction in non-crystalline systems

Abstract: A summary is given of what is now known about the existence of localized states for electrons in three-dimensional disordered systems, and what can be conjectured about the behaviour of the conductivity at zero temperature when this is finite but small

First direct observation of Dirac fermions in graphite

Abstract: Originating from relativistic quantum field theory, Dirac fermions have been invoked recently to explain various peculiar phenomena in condensed-matter physics, including the novel quantum Hall effect in graphene1,2, the magnetic-field-driven metal–insulator-like transition in graphite3,4, superfluidity in 3He (ref. 5) and the exotic pseudogap phase of high-temperature superconductors6,7. Despite their proposed key role in those systems, direct experimental evidence of Dirac fermions has been limited. Here, we report the first direct observation of relativistic Dirac fermions with linear dispersion near the Brillouin zone (BZ) corner H, which coexist with quasiparticles that have a parabolic dispersion near another BZ corner K. In addition, we also report a large electron pocket that we attribute to defect-induced localized states. Thus, graphite presents a system in which massless Dirac fermions, quasiparticles with finite effective mass and defect states all contribute to the low-energy electronic dynamics.

Evolution of the pseudogap from Fermi arcs to the nodal liquid

Abstract: The response of a material to external stimuli depends on its low-energy excitations. In conventional metals, these excitations are electrons on the Fermi surface—a contour in momentum (k) space that encloses all of the occupied states for non-interacting electrons. The pseudogap phase in the copper oxide superconductors, however, is a most unusual state of matter1. It is metallic, but part of its Fermi surface is ‘gapped out’ (refs 2, 3); low-energy electronic excitations occupy disconnected segments known as Fermi arcs4. Two main interpretations of its origin have been proposed: either the pseudogap is a precursor to superconductivity5, or it arises from another order competing with superconductivity6. Using angle-resolved photoemission spectroscopy, we show that the anisotropy of the pseudogap in k-space and the resulting arcs depend only on the ratio T/T*(x), where T*(x) is the temperature below which the pseudogap first develops at a given hole doping x. The arcs collapse linearly with T/T*(x) and extrapolate to zero extent as T→0. This suggests that the T=0 pseudogap state is a nodal liquid—a strange metallic state whose gapless excitations exist only at points in k-space, just as in a d-wave superconducting state.

Springer handbook of atomic, molecular, and optical physics

Abstract: Units and Constants- Part A Mathematical Methods: Angular Momentum Theory- Group Theory for Atomic Shells- Dynamical Groups- Perturbation Theory- Second Quantization- Density Matrices- Computational Techniques- Hydrogenic Wave Functions- Part B Atoms: Atomic Spectroscopy- High Precision Calculations for Helium- Atomic Multipoles- Atoms in Strong Fields- Rydberg Atoms- Rydberg Atoms in Strong Static Fields- Hyperfine Structure- Precision Oscillator Strength and Lifetime Measurements- Ion Beam Spectroscopy- Line Shapes and Radiation Transfer- Thomas - Fermi and Other Density-Functional Theories- Atomic Structure: Multiconfiguration Hartree - Fock Theories- Relativistic Atomic Structure- Many-Body Theory of Atomic Structure and Processes- Photoionization of Atoms- Autoionization- Green's Functions of Field Theory- Quantum Electrodynamics- Tests of Fundamental Physics- Parity Nonconserving Effects in Atoms- Atomic Clocks and Constraints on Variations of Fundamental Constants- Molecular Structure- Molecular Symmetry and Dynamics- Radiative Transition Probabilities- Molecular Photodissociation- Time-Resolved Molecular Dynamics- Nonreactive Scattering- Gas Phase Reactions- Gas Phase Ionic Reactions- Clusters- Infrared Spectroscopy- Laser Spectroscopy in the Submillimeter and Far-Infrared Region- Spectroscopic Techniques: Lasers- Spectroscopic Techniques: Cavity-Enhanced Methods- Spectroscopic Techniques: Ultraviolet- Part C Scattering Theory: Elastic Scattering: Classical, Quantal, and Semiclassical- Orientation and Alignment in Atomic and Molecular Collisions- Electron-Atom, Electron-Ion, and Electron-Molecule Collisions- Positron Collisions- Adiabatic and Diabatic Collision Processes at Low Energies- Ion -Atom and Atom - Atom Collisions- Ion - Atom Charge Transfer Reactions at Low Energies- Continuum Distorted-Wave and Wannier Methods- Ionization in High Energy Ion - Atom Collisions- Electron - Ion and Ion - Ion Recombination- Dielectronic Recombination- Rydberg Collisions: Binary Encounter, Born and Impulse Approximations- Mass Transfer at High Energies: Thomas Peak- Classical Trajectory and Monte Carlo Techniques- Collisional Broadening of Spectral Lines- Part D Scattering Experiments: Photodetachment- Photon - Atom Interactions: Low Energy- Photon - Atom Interactions: Intermediate Energies- Electron - Atom and Electron - Molecule Collisions- Ion - Atom Scattering Experiments: Low Energy- Ion - Atom Collisions:High Energy- Reactive Scattering- Ion - Molecule Reactions- Part E Quantum Optics: Light - Matter Interaction- Absorption and Gain Spectra- Laser Principles- Types of Lasers- Nonlinear Optics- Coherent Transients- Multiphoton and Strong-Field Processes- Cooling and Trapping- Quantum Degenerate Gases: Bose - Einstein Condensation- De Broglie Optics- Quantized Field Effects- Entangled Atoms and Fields: Cavity QED- Quantum Optical Tests of the Foundations of Physics- Quantum Information- Part F Applications: Applications of Atomic and Molecular Physics to Astrophysics- Comets- Aeronomy- Applications of Atomic and Molecular Physics to Global Change- Atoms in Dense Plasmas- Conduction of Electricity in Gases- Applications to Combustion- Surface Physics- Interface with Nuclear Physics- Charged-Particle - Matter Interactions- Radiation Physics- About the Authors- Subject Index

Overview of the RF source development programme at IPP Garching

Abstract: The development of a large-area RF source for negative hydrogen ions, an official EFDA task agreement, is aiming at demonstrating ITER-relevant ion source parameters. This implies a current density of 200?A?m?2 accelerated D? ions at a source filling pressure of ?0.3?Pa and an electron-to-ion ratio of ?1 from an extraction area similar to the positive-ion based sources at JET and ASDEX Upgrade and for pulse lengths of up to 1?h. The work is progressing along three lines in parallel: (i) optimization of current densities at low pressure and electron/ion ratio, utilizing small extraction areas (<0.01?m2) and short pulses (<6?s), in this parameter range the ITER requirements are met or even exceeded; (ii) investigation on extended extraction areas (<0.03?m2) and pulse lengths of up to 3600?s and (iii) investigation of a size-scaling on a half-size ITER plasma source. Three different test beds are being used to carry out these investigations in parallel. An extensive diagnostic and modelling programme accompanies the activities. The paper discusses the recent achievements and the status in these three areas of development.

New measurement of the electron magnetic moment using a one-electron quantum cyclotron.

Abstract: A new measurement resolves cyclotron and spin levels for a single-electron quantum cyclotron to obtain an electron magnetic moment, given by g/2=1.001 159 652 180 85 (76) [0.76 ppt]. The uncertainty is nearly 6 times lower than in the past, and g is shifted downward by 1.7 standard deviations. The new g, with a quantum electrodynamics (QED) calculation, determines the fine structure constant with a 0.7 ppb uncertainty--10 times smaller than for atom-recoil determinations. Remarkably, this 100 mK measurement probes for internal electron structure at 130 GeV.

Mode Locking of Electron Spin Coherences in Singly Charged Quantum Dots

Abstract: The fast dephasing of electron spins in an ensemble of quantum dots is detrimental for applications in quantum information processing. We show here that dephasing can be overcome by using a periodic train of light pulses to synchronize the phases of the precessing spins, and we demonstrate this effect in an ensemble of singly charged (In,Ga)As/GaAs quantum dots. This mode locking leads to constructive interference of contributions to Faraday rotation and presents potential applications based on robust quantum coherence within an ensemble of dots.

Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy.

Abstract: We study electron mobilities in nanoporous and single-crystal titanium dioxide with terahertz time domain spectroscopy. This ultrafast technique allows the determination of the electron mobility after carrier thermalization with the lattice but before equilibration with defect trapping states. The mobilities reported here for single-crystal rutile (1 cm2/(V s)) and porous TiO2 (10(-2) cm2/(V s)) therefore represent upper limits for electron transport at room temperature for defect-free materials. The large difference in mobility between bulk and porous samples is explained using Maxwell-Garnett effective medium theory. These results demonstrate that electron mobility is strongly dependent on the material morphology in nanostructured polar materials due to local field effects and cannot be used as a direct measure of the diffusion coefficient.

Demonstration of electron filtering to increase the Seebeck coefficient in In 0.53 Ga 0.47 As ∕ In 0.53 Ga 0.28 Al 0.19 As superlattices

Abstract: In this paper, we explore electron filtering as a technique to increase the Seebeck coefficient and the thermoelectric power factor of heterostructured materials over that of the bulk We present a theoretical model in which the Seebeck coefficient and the power factor can be increased in an ${\mathrm{In}}_{053}{\mathrm{Ga}}_{047}\mathrm{As}$-based composite material Experimental measurements of the cross-plane Seebeck coefficient are presented and confirm the importance of the electron filtering technique to decouple the electrical conductivity and Seebeck coefficient to increase the thermoelectric power factor

Interplay of electron–lattice interactions and superconductivity in Bi 2 Sr 2 CaCu 2 O 8+δ

Abstract: Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d2I/dV2 corresponds to each phonon mode1,2,3. For high-transition-temperature (high-Tc) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation4 and related electron–boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize. However, with the latest advances in d2I/dV2 spectroscopy using scanning tunnelling microscopy, it has become possible to study bosonic modes directly at the atomic scale5. Here we report d2I/dV2 imaging6,7,8 studies of the high-Tc superconductor Bi2Sr2CaCu2O8+δ. We find intense disorder of electron–boson interaction energies at the nanometre scale, along with the expected modulations in d2I/dV2 (refs 9, 10). Changing the density of holes has minimal effects on both the average mode energies and the modulations, indicating that the bosonic modes are unrelated to electronic or magnetic structure. Instead, the modes appear to be local lattice vibrations, as substitution of 18O for 16O throughout the material reduces the average mode energy by approximately 6 per cent—the expected effect of this isotope substitution on lattice vibration frequencies5. Significantly, the mode energies are always spatially anticorrelated with the superconducting pairing-gap energies, suggesting an interplay between these lattice vibration modes and the superconductivity.

Bidirectional Counting of Single Electrons

Abstract: A bidirectional single-electron counting device is demonstrated. Individual electrons flowing in forward and reverse directions through a double quantum dot are detected with a quantum point contact acting as a charge sensor. A comprehensive statistical analysis in the frequency and time domains and of higher order moments of noise reveals antibunching correlation in single-electron transport through the device itself. The device can also be used to investigate current flow in the attoampere range, which cannot be measured by existing current meters.

Measurement of the quantum capacitance of interacting electrons in carbon nanotubes

Abstract: The electronic capacitance of a one-dimensional system such as a carbon nanotube is a thermodynamic quantity that contains fundamental information about the ground state1. It is composed of an electrostatic component describing the interactions between electrons and their correlations, and a kinetic term given by the electronic density of states. Here, we use a field-effect transistor geometry to obtain the first direct capacitance measurement of individual carbon nanotubes, as a function of the carrier density. Our measurements detect the electrostatic part of the capacitance as well as the quantum corrections arising from the electronic density of states. We identify the van-Hove singularities that correspond to the one-dimensional electron and hole sub-bands and show that the measured capacitance exhibits clear electron–hole symmetry. Finally, our measurements suggest the existence of a negative capacitance, which has recently been predicted to exist in one dimension as a result of interactions between electrons2,3,4.