Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.Comment: SP and FK contributed equally to this wor

Multi-shell gold nanowires under compression

Deformation properties of multi-wall gold nanowires under compressive loading are studied. Nanowires are simulated using a realistic many-body potential. Simulations start from cylindrical fcc(111) structures at T=0 K. After annealing cycles axial compression is applied on multi-shell nanowires for a number of radii and lengths at T=300 K. Several types of deformation are found, such as large buckling distortions and progressive crushing. Compressed nanowires are found to recover their initial lengths and radii even after severe structural deformations. However, in contrast to carbon nanotubes irreversible local atomic rearrangements occur even under small compressions.Comment: 1 gif figure, 5 ps figure

Statistics of the Charging Spectrum of a Two-Dimensional Coulomb Glass Island

The fluctuations of capacitance of a two-dimensional island are studied in the regime of low electron concentration and strong disorder, when electrons can be considered classical particles. The universal capacitance distribution is found, with the dispersion being of the order of the average. This distribution is shown to be closely related to the shape of the Coulomb gap in the one-electron density of states of the island. Behavior of the the capacitance fluctuations near the metal - insulator transition is discussed.Comment: 4 pages, LaTex, 4 Postscript figures are included Discussion of the situation with screening by metallic gate is adde

Multiple Functionality in Nanotube Transistors

Calculations of quantum transport in a carbon nanotube transistor show that such a device offers unique functionality. It can operate as a ballistic field-effect transistor, with excellent characteristics even when scaled to 10 nm dimensions. At larger gate voltages, channel inversion leads to resonant tunneling through an electrostatically defined nanoscale quantum dot. Thus the transistor becomes a gated resonant tunelling device, with negative differential resistance at a tunable threshold. For the dimensions considered here, the device operates in the Coulomb blockade regime, even at room temperature.Comment: To appear in Phys. Rev. Let

Analytic results for NN particles with 1/r21/r^2 interaction in two dimensions and an external magnetic field

The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a $(2N-4)$-dimensional problem which is independent of $B$ and $\omega_0$. An exact, infinite set of relative mode excitations are obtained for any $N$. The $N=3$ problem reduces to that of a ficticious particle in a two-dimensional, non-linear potential of strength $\beta$, subject to a ficticious magnetic field $B_{\rm fic}\propto J$, the relative angular momentum.Comment: To appear in Physical Review Letters (in press). RevTeX file. Two figures available from [email protected] or [email protected]

Scanned Potential Microscopy of Edge and Bulk Currents in the Quantum Hall Regime

Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. In addition, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk currents in the QH regime.Comment: 4 pages, 5 figure

Conductance oscillations in tunnel-coupled quantum dots in the quantum Hall regime

We present measurements of transport through two tunnel-coupled quantum dots of different sizes connected in series in a strong, variable, perpendicular magnetic field. Double dot conductance was measured both as a function of magnetic field, which was varied across the filling factor nu = 4 quantum Hall plateau, and as a function of charge induced evenly on the two dots. The conductance peaks undergo position shifts and height modulations as the magnetic field is varied. These shifts and modulations form a pattern that repeats over large ranges of magnetic field and with the addition of double dot charge. The robust pattern repetition is consistent with a frequency locking effect.Comment: 12 pages, 4 figure

Correlation effects in a quantum dot at high magnetic fields

We investigate the effects of electron correlations on the ground state energy and the chemical potential of a droplet confined by a parabolic potential at high magnetic fields. We demonstrate the importance of correlations in estimating the transition field at which the first edge reconstruction of the maximum density droplet occurs in the spin polarized regime.Comment: 11 pages (revtex) 3 postscript figures are included at the end of the tex file. To appear in Phys. Rev.

Energetics of Quantum Antidot States in Quantum Hall Regime

We report experiments on the energy structure of antidot-bound states. By measuring resonant tunneling line widths as function of temperature, we determine the coupling to the remote global gate voltage and find that the effects of interelectron interaction dominate. Within a simple model, we also determine the energy spacing of the antidot bound states, self consistent edge electric field, and edge excitation drift velocity.Comment: 4 pages, RevTex, 5 Postscript figure

Absence of bimodal peak spacing distribution in the Coulomb blockade regime

Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in agreement with the experimental observations. We attribute this behavior to the tendency of an even number of electrons to gain on-site interaction energy by removing the spin degeneracy. Thus, the dot is predicted to show a non trivial electron number dependent spin polarization. Experimental test of this hypothesis based on the spin polarization measurements are proposed.Comment: 13 pages, 3 figures, accepted for publication in PRL - a few small change