Coulomb Charging Effects Research Articles

Quantum Hall Interferometry in Triangular Domains of Marginally Twisted Bilayer Graphene.

Quantum Hall (QH) interferometry provides an archetypal platform for the experimental realization of braiding statistics of fractional QH states. However, the complexity of observing fractional statistics requires phase coherence over the length of the interferometer, as well as suppression of Coulomb charging energy. Here, we demonstrate a new type of QH interferometer based on marginally twisted bilayer graphene (mtBLG), with a twist angle θ ≈ 0.16°. With the device operating in the QH regime, we observe distinct signatures of electronic Fabry-Pérot and Aharonov-Bohm oscillations of the magneto-thermopower in the density-magnetic field phase space, at Landau level filling factors ν = 4, 8. We find that QH interference effects are intrinsic to the triangular AB/BA domains in mtBLG that show diminished Coulomb charging effects. Our results demonstrate phase-coherent interference of QH edge modes without any additional gate-defined complex architecture, which may be beneficial in experimental realizations of non-Abelian braiding statistics.

Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation

Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases.

Measurement and control of a Coulomb-blockaded parafermion box

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.

Local charge trapping in Ge nanoclustersdetected by Kelvin probe force microscopy

The understanding of local charge trapping on the nanoscale is crucial for the design of novel electronic devices and photodetectors based on SiGe nanoclusters (NCs). Here, the local spatial distribution of the surface potential of the Ge NCs was detected using Kelvin probe force microscopy (KPFM). Different surface potentials between Ge NCs and the wetting layer (WL) surface were detected at room temperature. Changes of the local contact potential differences (CPD) were studied after injection of electrons or holes into single Ge NCs on top of the Si layer using a conductive atomic force microscopy tip. The CPD image contrast was increased after electron injection by applying a forward bias to the n-tip/i-Ge NC/p-Si junction. Injecting holes into a single Ge NC was also accompanied by filling of two-dimensional states in the surrounding region, which is governed by leakage currents through WL or surface states and Coulomb charging effects. A long retention time of holes trapped by the Ge NC was found.

On the single‐particle‐reduced entropy of a gated nanowire system in the Coulomb blockade regime

Abstractmagnified imageIn this Letter, the single‐particle‐reduced entropy of a nanowire field‐effect transistor (NWFET) in the Coulomb blockade regime is studied by means of a multi‐configura‐tional self‐consistent Green's function approach. Assuming that the many‐body statistical preparation of the system is described by a mixture of Slater determinants of relevant natural orbitals, the single‐particle‐reduced entropy can be interpreted as a measure of the degree of mixture of the system's preparation. Considering the realistic case of an InP based NWFET, we present current–voltage characteristics and entropy diagrams for a range of equilibrium and non‐equilibrium states. Signatures of few‐electron Coulomb charging effects can be identified, as known from experimental situations. Furthermore, we illustrate the significance of the single‐particle‐reduced entropy by analyzing the corresponding electronic configurations. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Crossover from two- to three-dimensional gold particle shapes on CaO films of different thicknesses

The growth of Au particles on Mo(001)-supported CaO films has been investigated as a function of film thickness by means of scanning tunneling microscopy and spectroscopy. Whereas, monolayer Au islands develop in the low-thickness regime [1--25 monolayers (ML)], formation of three-dimensional (3D) deposits is revealed above 40-ML film thickness. The two-dimensional (2D) growth morphology is ascribed to a charge transfer out of the CaO/Mo support into the adparticles, resulting in a reinforcement of the Au-CaO interface interaction and a strong preference for a wetting growth of gold. In the limit of ultrathin films, this charge transfer is governed by electron tunneling from the Mo substrate into the Au islands and is driven by the different Fermi levels of both systems. Although tunneling transport breaks down beyond 5--10-ML film thickness, the signature of charge-mediated Au growth remains detectable for even thicker films. This finding suggests the presence of intrinsic charge centers in the CaO film that are able to donate electrons to the gold. We relate these donor centers to Mo ions that spontaneously have diffused from the Mo support into the CaO lattice during growth. Given the low mobility of Mo in the oxide matrix, the donor concentration diminishes with film thickness and, hence, the ability of the CaO to transfer electrons into the Au deposits. Consequently, the 2D growth behavior of Au changes into the 3D regime that is characteristic for metals on inert oxide surfaces. Spectroscopic characterization of the Au particles revealed pronounced electron quantization and Coulomb charging effects due to the reduced island size.

Coulomb blockade of Majorana-fermion-induced transport

We study Coulomb charging effects for transport through a topologically nontrivial superconducting wire, where Majorana bound states are present at the interface to normal-conducting leads. We construct the general Keldysh functional integral representation, and provide detailed results for the nonlinear current-voltage relation under weak Coulomb blockade conditions.

Coulomb charging effect of electrons in InAs/InAlAs quantum dots studied by capacitance techniques

Capacitance–voltage and deep level transient spectroscopy were used to study the capture characteristics of self-assembled InAs/InAlAs quantum dots grown on the InP substrate. It is found that the number of electrons captured by quantum dots can be controlled by varying the width of applied pulse voltage in the DLTS measurements. The Coulomb charging energy and the time of capture can be deduced from the filling time dependent deep level transient spectra.

On the application potential of gold nanoparticles in nanoelectronics and biomedicine

Ligand-stabilized gold nanoparticles (AuNPs) are of high interest to research dedicated to future technologies such as nanoelectronics or biomedical applications. This research interest arises from the unique size-dependent properties such as surface plasmon resonance or Coulomb charging effects. It is shown here how the unique properties of individual AuNPs and AuNP assemblies can be used to create new functional materials for applications in a technical or biological environment. While the term technical environment focuses on the potential use of AuNPs as subunits in nanoelectronic devices, the term biological environment addresses issues of toxicity and novel concepts of controlling biomolecular reactions on the surface of AuNPs.

Bias spectroscopy and simultaneous single-electron transistor charge state detection of Si:Pdouble dots

We report a detailed study of low-temperature (mK) transport properties of a silicondouble-dot system fabricated by phosphorous ion implantation. The device under studyconsists of two phosphorous nanoscale islands doped to above the metal–insulatortransition, separated from each other and the source and drain reservoirs by nominallyundoped (intrinsic) silicon tunnel barriers. Metallic control gates, together with anAl–AlOx single-electron transistor (SET), were positioned on the substrate surface,capacitively coupled to the buried dots. The individual double-dot charge stateswere probed using source–drain bias spectroscopy combined with non-invasiveSET charge sensing. The system was measured in linear (source–drain DC biasVSD = 0) and non-linear (VSD ≠ 0) regimes, allowing calculations of the relevant capacitances. Simultaneous detection usingboth SET sensing and source–drain current measurements was demonstrated, providing avaluable combination for the analysis of the system. Evolution of the triple points withapplied bias was observed using both charge and current sensing. Coulomb diamonds,showing the interplay between the Coulomb charging effects of the two dots, weremeasured using simultaneous detection and compared with numerical simulations.

Understanding Coulomb Effects in Nanoscale Schottky-Barrier-FETs

We employ a novel multiconfigurational self-consistent Green's function approach (MCSCG) for the simulation of nanoscale Schottky-barrier-field-effect transistors (SB-FETs). This approach allows the calculation of electronic transport with a seamless transition from the single-electron regime to room-temperature FET operation. The particular improvement of the MCSCG stems from a self-consistent division of the channel system into a small subsystem of resonantly trapped states for which a many-body Fock space approach becomes numerically feasible and the rest of the system which can be treated adequately on a conventional mean-field level. The Fock space description allows for the calculation of few-electron Coulomb charging effects beyond the mean-field. We compare a conventional Hartree nonequilibrium Green's function calculation with the results of the MCSCG approach. Using the MCSCG method, Coulomb blockade effects are demonstrated at low temperatures while, under strong nonequilibrium and high-temperature conditions, the Hartree approximation is retained. Finally, the visibility of quantum and single-electron effects in scaled transistor structures is discussed

Quantum confinement corrections to the capacitance of gated one-dimensional nanostructures

With the help of a multi-configurational Green's function approach we simulate single-electron Coulomb charging effects in gated ultimately scaled nanostructures which are beyond the scope of a selfconsistent mean-field description. From the simulated Coulomb-blockade characteristics we derive effective system capacitances and demonstrate how quantum confinement effects give rise to corrections. Such deviations are crucial for the interpretation of experimentally determined capacitances and the extraction of application-relevant system parameters.

Study of coupling effect in double-layer quantum dots by admittance spectroscopy

The influence of the coupling effect on quantum confinement energy levels and on the Coulomb charging effect in double-layer GeSi quantum dots (QDs) is investigated by admittance spectroscopy. The coupling effect depends on the thickness of the space layer between QD layers. The increasing Coulomb charging energy observed in QD samples with different thickness (4.5, 6, and 7.5nm) indicates that the coupling effect can weaken the quantum confinement effect and Coulomb charging interaction. When the space layer is thicker than 7.5nm, the influence of the coupling effect can be neglected.

Coherent Transport of Hole and Coulomb Blockade Phenomenon in Long p-Type Semiconductor Carbon Nanotube

We have succeeded in observing the coexistence of the Coulomb charging effect and the coherent transport of the hole in a single-walled carbon nanotube (SWNT) with a length of 4.5 µm at 8.6 K. SWNT channel field-effect transistor (FET) structures were prepared with two different channel lengths of 4.5 and 1.4 µm. The samples showed p-type semiconductor characteristics under large gate and drain biases at 8.6 K. At 8.6 K, on the other hand, single-hole transistor characteristics with different Coulomb charging energies corresponding to the length of the channel were observed in each sample. Drain current peaks with different periods corresponding to the length of the channel were also observed outside of the Coulomb blockade area for the higher drain voltages in each sample. The drain current peaks are attributed to resonant tunneling of the hole through the separation of the quantum energy levels originating from coherent transport of the hole in the entire semiconductive SWNT.

The electronic dynamics of a coupled-quantum-dot structure driven by an AC field

We theoretically investigate electronic dynamic behavior in a coupled-quantum-dot structure driven by an AC field. Based on the density-matrix theory, the time evolution of the electron occupation probability is shown by solving a coupled nonlinear equation in combination with Coulomb charging effect. The AC field leads to the changes of the oscillation behavior of the electron, which is investigated in several frequency regions. The field at a certain frequency can induce the transition of suppression and enhancement of the electronic delocalization with various Coulomb charging energy. But in very high-frequency, the field has little effect on the electronic dynamics. In the region of photon-assisted tunneling, the minimal time for the electron tunneling to the other dot decreases with increasing the frequency of the field. In addition, the Coulomb charging energy enhances the dynamical suppression of electronic delocalization. The strong electronic localization is found in the weak coupling quantum dots. The results show that a single-electron switch may be realized in the structure.

Size-dependent resonant tunneling and storing of electrons in a nanocrystalline silicon floating-gate double-barrier structure

We use frequency-dependent capacitance spectroscopy to study electron tunneling and storing in nanocrystalline silicon (nc-Si) floating-gate double-barrier structure (SiO2/nc-Si/SiO2) fabricated in situ by plasma oxidation and layer-by-layer deposition in a plasma-enhanced chemical vapor deposition system. Distinct size- and frequency-dependent capacitance peaks due to Coulomb blockade charging and quantum-confinement effects have been observed by capacitance spectroscopy in a large ensemble of nc-Si dots at room temperature for the first time in a SiO2/nc-Si/SiO2 system. This finding demonstrates that the Coulomb blockade for electrons in nc-Si dots is larger than the size fluctuation effects on the quantum confinement for our nc-Si floating-gate double-barrier structure.

Investigation of the quantum confinement effects in Ge dots by electrical measurements

The quantum confinement effects of Ge quantum-dots (QDs) grown by molecular beam epitaxy (MBE) are investigated by capacitance–voltage ( C–V), admittance spectroscopy, and deep level transient spectroscopy (DLTS). The potential height of hole in the Ge dot obtained by C–V intercept, admittance spectroscopy and DLTS are 0.335, 0.341, and 0.338 eV, respectively. The DLTS method is also used to observe the changes of hole concentration, activation energy ( E a), and capture cross-section with filling time duration ( t p) and bias voltage. The results show that the hole concentration in the Ge quantum-dots is a function of the pulse duration ( t p) and reversed bias voltage, the activation energy and capture cross-section decrease with the increasing filling time duration due to the Coulomb charging effect.

Single-electron transistor of a single organic molecule with access to several redox states.

A combination of classical Coulomb charging, electronic level spacings, spin, and vibrational modes determines the single-electron transfer reactions through nanoscale systems connected to external electrodes by tunnelling barriers. Coulomb charging effects have been shown to dominate such transport in semiconductor quantum dots, metallic and semiconducting nanoparticles, carbon nanotubes, and single molecules. Recently, transport has been shown to be also influenced by spin--through the Kondo effect--for both nanotubes and single molecules, as well as by vibrational fine structure. Here we describe a single-electron transistor where the electronic levels of a single pi-conjugated molecule in several distinct charged states control the transport properties. The molecular electronic levels extracted from the single-electron-transistor measurements are strongly perturbed compared to those of the molecule in solution, leading to a very significant reduction of the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. We suggest, and verify by simple model calculations, that this surprising effect could be caused by image charges generated in the source and drain electrodes resulting in a strong localization of the charges on the molecule.

Cross-linked PMMA as a low-dimensional dielectric sacrificial layer

A surface nanomachining fabrication process using electron beam cross-linked poly(methyl) methacrylate (PMMA) has been developed and characterized. PMMA with different molecular weights (MW 100 K, MW 495 K, MW 950 K) in anisole casting solvent has been crosslinked with different electron beam irradiation levels ranging from 20 C/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> to 240 C/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This is to investigate the quantifiable relationship between electron dose and its submicrometer remaining thickness after dissolving in acetone. This technique which uses electron beam lithography, offers a high resolution semi-three-dimensional (3-D) nanomachining of the sacrificial layer in a single run. Because of its low Young's modulus, it has been successfully integrated with nanoelectromechanical systems processing and has the advantage of producing low-stress submicrometer thick structures with lateral dimensions as low as, but not limited to 1 μm. A fast dry release time from 55 to 100 s using oxygen plasma ashing has been demonstrated for a sacrificial layer aspect ratio of 125. This corresponds to an etch rate of about 0.6 μm/s at an average temperature of 40°C. The success of using cross-linked PMMA as a gate dielectric is demonstrated by the fabrication of multilayered gated lateral quantum dot devices. Periodic and continuous conductance oscillations arising from Coulomb charging effects are clearly observed in the transport properties at 50 mK.

Shot noise in tunneling transport through molecules and quantum dots

We consider electrical transport through single molecules coupled to metal electrodes via tunneling barriers. Approximating the molecule by the Anderson-impurity model as the simplest model which includes Coulomb charging effects, we extend the ``orthodox'' theory to expand current and shot noise systematically order by order in the tunnel couplings. In particular, we show that a combined measurement of current and shot noise reveals detailed information of the system even in the weak-coupling limit, such as the ratio of the tunnel-coupling strengths of the molecule to the left and right electrodes, and the presence of the Coulomb charging energy. Our analysis holds for single-level quantum dots as well.