Coulomb Blockade Peak Research Articles

Single electron pumping through a quantum dot-embedded carbon nanotube using surface acoustic wave

We have studied acoustoelectric current through a quantum dot-embedded carbon nanotube induced by a surface acoustic wave. The measurements were carried out on a same device but in two very different quantum dot charging energy Ec regimes (∼50 and ∼5 meV). The results showed dramatic differences in induced acoustoelectric current depending on Ec. The induced acoustoelectric current showed a polarity reversal around the Coulomb blockade peak when Ec is small (5 meV). For a large Ec (50 meV), however, a current plateau was observed as a function of surface acoustic wave powers as well as gate voltages.

Coherent destruction of Coulomb blockade peaks in molecular junctions

Coherent electronic transport in single-molecule junctions is investigated in the Coulomb blockade regime. Both the transmission phase and probability are calculated for junctions with various contact symmetries. A dramatic suppression of the Coulomb blockade peaks is predicted for junctions where multiple atomic orbitals of the molecule couple to a single electrode although the charging steps are unaffected.

Interaction-Induced Spin Polarization in Quantum Dots

The electronic states of lateral many-electron quantum dots in high magnetic fields are analyzed in terms of energy and spin. In a regime with two Landau levels in the dot, several Coulomb-blockade peaks are measured. A zigzag pattern is found as it is known from the Fock-Darwin spectrum. However, only data from Landau level 0 show the typical spin-induced bimodality, whereas features from Landau level 1 cannot be explained with the Fock-Darwin picture. Instead, by including the interaction effects within spin-density-functional theory a good agreement between experiment and theory is obtained. The absence of bimodality on Landau level 1 is found to be due to strong spin polarization.

Transition to Landau levels in graphene quantum dots

We investigate the electronic eigenstates of graphene quantum dots of realistic size (up to 80 nm diameter) in the presence of a perpendicular magnetic field $B$. Numerical tight-binding calculations and Coulomb-blockade measurements performed near the Dirac point exhibit the transition from the linear density of states at $B=0$ to the Landau-level regime at high fields. Details of this transition sensitively depend on the underlying graphene lattice structure, bulk defects, and localization effects at the edges. Key to the understanding of the parametric evolution of the levels is the strength of the valley-symmetry-breaking $K\text{\ensuremath{-}}{K}^{\ensuremath{'}}$ scattering. We show that the parametric variation in the level variance provides a quantitative measure for this scattering mechanism. We perform measurements of the parametric motion of Coulomb-blockade peaks as a function of magnetic field and find good agreement. We demonstrate that the magnetic-field dependence of graphene energy levels may serve as a sensitive indicator for the properties of graphene quantum dots and, in further consequence, for the validity of the Dirac picture.

Energy levels of few-electron quantum dots imaged and characterized by atomic force microscopy

Strong confinement of charges in few-electron systems such as in atoms, molecules, and quantum dots leads to a spectrum of discrete energy levels often shared by several degenerate states. Because the electronic structure is key to understanding their chemical properties, methods that probe these energy levels in situ are important. We show how electrostatic force detection using atomic force microscopy reveals the electronic structure of individual and coupled self-assembled quantum dots. An electron addition spectrum results from a change in cantilever resonance frequency and dissipation when an electron tunnels on/off a dot. The spectra show clear level degeneracies in isolated quantum dots, supported by the quantitative measurement of predicted temperature-dependent shifts of Coulomb blockade peaks. Scanning the surface shows that several quantum dots may reside on what topographically appears to be just one. Relative coupling strengths can be estimated from these images of grouped coupled dots.

Coulomb blockade doppelgängers in quantum Hall states

In this paper, we ask the question: how well can Coulomb blockade experiments correctly identify and distinguish between different topological orders in quantum Hall states? We definitively find the answer to be: quite poorly. In particular, we write the general expression for the spacing of resonance peaks in a simple form that explicitly displays its dependence on the conformal scaling dimensions of the systems' edge modes. This form makes transparent the general argument that the Coulomb blockade peak spacings do not provide a strongly indicative signature of the topological order of the system since it is only weakly related to the braiding statistics. We bolster this general argument with examples for all the most physically relevant non-Abelian candidate states, demonstrating that they have Coulomb blockade doppelg\"angers--candidate states at the same filling fraction with identical Coulomb blockade signatures but dramatically different topological orders and braiding statistics.

Imaging and manipulating electrons in a one-dimensional quantum dot with Coulomb blockade microscopy

Motivated by recent experiments by the Westervelt group, which used a mobile tip to probe the electronic state of a segmented nanowire, we calculate shifts in Coulomb blockade peak positions, as a function of tip location, which we term ``Coulomb blockade microscopy.'' We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high-density electronic liquid state from a Wigner-crystal state by microscopy with a weak-tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one-particle potential and kinetic energies. Finally, we propose that a weak-tip Coulomb blockade micrograph focusing on the transition between electron number $N=0$ and $N=1$ states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.

AlGaAs/GaAs single electron transistor fabricated without modulation doping

We have fabricated a quantum dot single electron transistor, based on AlGaAs/GaAs heterojunction without modulation doping, which exhibits clear and stable Coulomb blockade oscillations. The temperature dependence of the Coulomb blockade peak line shape is well described by standard Coulomb blockade theory in the quantum regime. Bias spectroscopy measurements have allowed us to directly extract the charging energy, and showed clear evidence of excited state transport, confirming that individual quantum states in the dot can be resolved.

Electron spin blockade and singlet-triplet transition in a silicon single electron transistor

We investigate a silicon single electron transistor in a metal-oxide-semiconductor structure by applying a magnetic field perpendicular to the sample surface. The quantum dot is defined electrostatically in a point-contact channel and by potential barriers probably from negatively charged interface traps. The magnetic field dependence of the excitation spectrum mostly can be attributed to the Zeeman effect. In the two-electron singlet-triplet (ST) transition, electron-electron Coulomb interaction plays a significant role. The evolution of Coulomb blockade peak positions with magnetic field $B$ is also owing to the Zeeman splitting with no obvious orbital effect up to 9 T. The filling pattern shows an alternate spin-up-spin-down sequence. The observed amplitude spectrum can be explained by the spin-blockade effect. When the two-electron system forms a singlet state at low magnetic fields, and the injection current from the lead becomes spin-down polarized, the tunneling conductance is reduced by a factor of 8. At higher fields, due to the ST transition, the spin-blockade effect is lifted and the conductance is fully recovered.

Effects of inter-group correlations on sequential electron transitions through redox-mediated two-center electrochemical bridged contact

A consistent method for the calculation of the electric current through a redox-mediated electrochemical tunnel contact with two redox groups in the bridge molecule is presented for the sequential mechanism of electron transfer in the limit of infinitely large Coulomb repulsion between the electrons located in the same redox group. It is shown that the kinetic inter-group correlation exists which results in general in the deviation of exact solution from the approximate “quasi-chemical approach” even in the absence of inter-group Coulomb repulsion. The increase of the latter leads to the appearance of the electron correlation effects which result, in particular, in the second maximum (Coulomb blockade peak) in the current/overvoltage dependence.

Graphene quantum dots: Beyond a Dirac billiard

We present realistic simulations of quantum confinement effects in phase-coherent graphene quantum dots with linear dimensions of 10--40 nm. We determine wave functions and energy-level statistics in the presence of disorder resulting from edge roughness, charge impurities, or short-ranged scatterers. Marked deviations from a simple Dirac billiard for massless fermions are found. We find a remarkably stable dependence of the nearest-neighbor level spacing on edge roughness suggesting that the roughness of fabricated devices can be possibly characterized by the distribution of measured Coulomb blockade peaks.

Quantum chaos in graphene nanoribbon quantum dot

The electron transport property of a graphene nanoribbon （GNR） quantum dot in a dilution refrigerator at temperature 20 mK is studied. The Coulomb blockade diamonds and excited energy levels of the quantum dot are clearly observed. It is found that the statistical distribution of the spacing between the nearest-neighboring Coulomb blockade peaks and that of the individual peak height are consistent respectively with the typical Wigner-Dyson distribution and Porter-Thomas distribution as prescribed by the random matrix theory for a quantum chaotic system. Thus， our results demonstrate that the GNR quantum dot is a quantum chaotic system at low temperatures. The possible origin of this phenomenon is also discussed.

Adiabatic Charge Pumping in Carbon Nanotube Quantum Dots

We investigate charge pumping in carbon nanotube quantum dots driven by the electric field of a surface acoustic wave. We find that, at small driving amplitudes, the pumped current reverses polarity as the conductance is tuned through a Coulomb blockade peak using a gate electrode. We study the behavior as a function of wave amplitude, frequency, and direction and develop a model in which our results can be understood as resulting from adiabatic charge redistribution between the leads and quantum dots on the nanotube.

Asymmetric Coulomb blockade and Kondo temperature of single-molecule transistors

Recent experiments on single-molecule transistors made of cobalt complexes exhibited anomalously weak gate voltage dependence of the Kondo temperature accompanied by a strong asymmetry in the Coulomb blockade peaks. We show that these observations can both be explained by strong electron–vibron interactions when including anharmonicities of the molecular potential surfaces. The strong electron–vibron interactions may originate from a tendency of the cobalt complexes toward Jahn–Teller distortion.

Chaotic Dirac Billiard in Graphene Quantum Dots

The exceptional electronic properties of graphene, with its charge carriers mimicking relativistic quantum particles and its formidable potential in various applications, have ensured a rapid growth of interest in this new material. We report on electron transport in quantum dot devices carved entirely from graphene. At large sizes (>100 nanometers), they behave as conventional single-electron transistors, exhibiting periodic Coulomb blockade peaks. For quantum dots smaller than 100 nanometers, the peaks become strongly nonperiodic, indicating a major contribution of quantum confinement. Random peak spacing and its statistics are well described by the theory of chaotic neutrino billiards. Short constrictions of only a few nanometers in width remain conductive and reveal a confinement gap of up to 0.5 electron volt, demonstrating the possibility of molecular-scale electronics based on graphene.

Coulomb blockade in graphene nanodisks

Graphene nanodisk is a graphene derivative with a closed edge. The trigonal zigzag nanodisk with size $N$ contains a zero-energy sector with the $\text{SU}(N)$ symmetry. We investigate electron-electron interaction effects within the zero-energy sector. We explicitly derive the direct and exchange interactions, which explicitly break the $\text{SU}(N)$ symmetry. Then, by regarding a nanodisk as a quantum dot with an internal degree of freedom, we analyze the nanodisk-lead system consisting of a nanodisk and two leads. By employing the standard Green's function method, we reveal Coulomb blockade effects in this system. As the chemical potential increases, a peculiar series of plateaux and dips develops in the occupation number and a peculiar series of Coulomb blockade peaks develops in the conductance, which reflect the energy spectrum of a nanodisk with a broken $\text{SU}(N)$ symmetry. It is argued that dips emerge in the occupation number due to a Coulomb correlation effect and that tiny Coulomb blockade peaks emerge due to a tunneling effect between the nanodisk and leads.

Transport properties of double-walled carbon nanotube quantum dots

The transport properties of quantum dot (QD) systems based on double-walled carbon nanotubes (DWCNTs) are investigated. The interplay between microscopic structure and strong Coulomb interaction is treated within a bosonization framework. The linear and nonlinear current-voltage characteristics of the QD system are calculated by starting from the Liouville equation for the reduced density matrix. Depending on the intershell couplings, an eight-electron periodicity of the Coulomb blockade peak spacing in the case of commensurate DWCNT QDs and a four-electron periodicity in the incommensurate case are predicted. The contribution of excited states of DWCNTs to the nonlinear transport is investigated as well.

Enhancing the conductance of a two-electron nanomechanical oscillator

We consider electron transport through a mobile island (i.e., a nanomechanical oscillator) which can accommodate one or two excess electrons and show that, in contrast to immobile islands, the Coulomb blockade peaks, associated with the first and second electrons entering the island, have different functional dependences on the nano-oscillator parameters when the island coupling to its leads is asymmetric. In particular, the conductance for the second electron (i.e., when the island is already charged) is greatly enhanced in comparison to the conductance of the first electron in the presence of an external electric field. We also analyze the temperature dependence of the two conduction peaks and show that these exhibit different functional behaviors.

Scanned Probe Imaging of Quantum Dots inside InAs Nanowires

We show how a scanning probe microscope (SPM) can be used to image electron flow through InAs nanowires, elucidating the physics of nanowire devices on a local scale. A charged SPM tip is used as a movable gate. Images of nanowire conductance versus tip position spatially map the conductance of InAs nanowires at liquid-He temperatures. Plots of conductance versus backgate voltage without the tip present show complex patterns of Coulomb-blockade peaks. Images of nanowire conductance identify their source as multiple quantum dots formed by disorder along the nanowire--each dot is surrounded by a series of concentric rings corresponding to Coulomb blockade peaks. An SPM image locates the dots and provides information about their size. In this way, SPM images can be used to understand the features that control transport through nanowires. The nanowires were grown from metal catalyst particles and have diameters approximately 80 nm and lengths 2-3 microm.

Electric-field control of tunneling magnetoresistance effect in a Ni∕InAs∕Ni quantum-dot spin valve

The authors demonstrate an electric-field control of tunneling magnetoresistance (TMR) effect in a semiconductor quantum-dot spin-valve device. By using ferromagnetic Ni nanogap electrodes, they observe the Coulomb blockade oscillations at a small bias voltage. In the vicinity of the Coulomb blockade peak, the TMR effect is significantly modulated and even its sign is switched by changing the gate voltage, where the sign of the TMR value changes at the resonant condition.