Counting statistics for electron capture in a dynamic quantum dot

One-Lead Single-Electron Source with Charging Energy

Single-electron sources, formed by a quantum dot (QD), are key elements for realizing electron analogue of quantum optics. We develop a new type of single-electron source with functionalities that are absent in existing sources. This source couples with only one lead. By an AC rf drive, it successively emits holes and electrons cotraveling in the lead, as in the mesoscopic capacitor. Thanks to the considerable charging energy of the QD, however, emitted electrons have energy levels a few tens of millielectronvolts above the Fermi level, so that emitted holes and electrons are split by a potential barrier on demand, resulting in a rectified quantized current. The resulting pump map exhibits quantized triangular islands, in good agreement with our theory. We also demonstrate that the source can be operated with another tunable-barrier single-electron source in a series double QD geometry, showing parallel electron pumping by a common gate driving.

Multi-Particle Interference in an Electronic Mach-Zehnder Interferometer

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.

Top-down GaN nanowire transistors with nearly zero gate hysteresis for parallel vertical electronics

This paper reports on the direct qualitative and quantitative performance comparisons of the field-effect transistors (FETs) based on vertical gallium nitride nanowires (GaN NWs) with different NW numbers (i.e., 1–100) and diameters (i.e., 220–640 nm) fabricated on the same wafer substrate to prove the feasibility of employing the vertical 3D architecture concept towards massively parallel electronic integration, particularly for logic circuitry and metrological applications. A top-down approach combining both inductively coupled plasma dry reactive ion etching (ICP-DRIE) and wet chemical etching is applied in the realization of vertically aligned GaN NWs on metalorganic vapor-phase epitaxy (MOVPE)-based GaN thin films with specific doping profiles. The FETs are fabricated involving a stack of n-p-n GaN layers with embedded inverted p-channel, top drain bridging contact, and wrap-around gating technology. From the electrical characterization of the integrated NWs, a threshold voltage (V_th) of (6.6 ± 0.3) V is obtained, which is sufficient for safely operating these devices in an enhancement mode (E-mode). Aluminium oxide (Al₂O₃) grown by atomic layer deposition (ALD) is used as the gate dielectric material resulting in nearly-zero gate hysteresis (i.e., forward and backward sweep V_th shift (ΔV_th) of ~0.2 V). Regardless of the required device processing optimization for having better linearity profile, the upscaling capability of the devices from single NW to NW array in terms of the produced currents could already be demonstrated. Thus, the presented concept is expected to bridge the nanoworld into the macroscopic world, and subsequently paves the way to the realization of innovative large-scale vertical GaN nanoelectronics.

Gigahertz Single-Electron Pumping Mediated by Parasitic States

In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz the accuracy typically decreases. Recently, hybrid pumps based on QDs coupled to trap states have led to increased transfer rates due to tighter electrostatic confinement. Here, we operate a hybrid electron pump in silicon obtained by coupling a QD to multiple parasitic states and achieve robust current quantization up to a few gigahertz. We show that the fidelity of the electron capture depends on the sequence in which the parasitic states become available for loading, resulting in distinctive frequency-dependent features in the pumped current.

High-accuracy current generation in the nanoampere regime from a silicon single-trap electron pump

A gigahertz single-electron (SE) pump with a semiconductor charge island is promising for a future quantum current standard. However, high-accuracy current in the nanoampere regime is still difficult to achieve because the performance of SE pumps tends to degrade significantly at frequencies exceeding 1 GHz. Here, we demonstrate robust SE pumping via a single-trap level in silicon up to 7.4 GHz, at which the pumping current exceeds 1 nA. An accuracy test with an uncertainty of about one part per million (ppm) reveals that the pumping current deviates from the ideal value by only about 20 ppm at the flattest part of the current plateau. This value is two orders of magnitude better than the best one reported in the nanoampere regime. In addition, the pumping accuracy is almost unchanged up to 7.4 GHz, probably due to strong electron confinement in the trap. These results indicate that trap-mediated SE pumping is promising for achieving the practical operation of the quantum current standard.

Dynamics of a single-atom electron pump

Single-electron pumps based on isolated impurity atoms have recently been experimentally demonstrated. In these devices the Coulomb potential of an atom creates a localised electron state with a large charging energy and considerable orbital level spacings, enabling robust charge capturing processes. In contrast to the frequently used gate-defined quantum dot pumps, which experience a strongly time-dependent potential, the confinement potential in these single-atom pumps is hardly affected by the periodic driving of the system. Here we describe the behaviour and performance of an atomic, single parameter, electron pump. This is done by considering the loading, isolating and unloading of one electron at the time, on a phosphorous atom embedded in a silicon double gate transistor. The most important feature of the atom pump is its very isolated ground state, which is populated through the fast loading of much higher lying excited states and a subsequent fast relaxation process. This leads to a substantial increase in pumping accuracy, and is opposed to the adverse role of excited states observed for quantum dot pumps due to non-adiabatic excitations. The pumping performance is investigated as a function of dopant position, revealing a pumping behaviour robust against the expected variability in atomic position.

Three-waveform bidirectional pumping of single electrons with a silicon quantum dot

Semiconductor-based quantum dot single-electron pumps are currently the most promising candidates for the direct realization of the emerging quantum standard of the ampere in the International System of Units. Here, we discuss a silicon quantum dot single-electron pump with radio frequency control over the transparencies of entrance and exit barriers as well as the dot potential. We show that our driving protocol leads to robust bidirectional pumping: one can conveniently reverse the direction of the quantized current by changing only the phase shift of one driving waveform with respect to the others. We anticipate that this pumping technique may be used in the future to perform error counting experiments by pumping the electrons into and out of a reservoir island monitored by a charge sensor.

Ultrafast Emission and Detection of a Single-Electron Gaussian Wave Packet: A Theoretical Study

Generating and detecting a prescribed single-electron state is an important step towards solid-state fermion optics. We propose how to generate an electron in a Gaussian state, using a quantum-dot pump with gigahertz operation and realistic parameters. With the help of a strong magnetic field, the electron occupies a coherent state in the pump, insensitive to the details of nonadiabatic evolution. The state changes during the emission from the pump, governed by competition between the Landauer-Buttiker traversal time and the passage time. When the former is much shorter than the latter, the emitted state is a Gaussian wave packet. The Gaussian packet can be identified by using a dynamical potential barrier, with a resolution reaching the Heisenberg minimal uncertainty ℏ/2.

Non-adiabatic quantized charge pumping with tunable-barrier quantum dots: a review of current progress

Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property--the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of [Formula: see text] as function of control parameters, where [Formula: see text] is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots.

Quantum Phase Coherence in Mesoscopic Transport Devices with Two-Particle Interaction

In this paper we demonstrate a new type of quantum phase coherence (QPC), which is generated by the two-body interaction. This conclusion is based on quantum master equation analysis for the full counting statistics of electron transport through two parallel quantum-dots with antiparallel magnetic fluxes in order to eliminate the Aharonov-Bohm interference of either single-particle or non-interacting two-particle wave functions. The interacting two-particle QPC is realized by the flux-dependent oscillation of the zero-frequency cumulants including the shot noise and skewness with a characteristic period. The accurately quantized peaks of cumulant spectrum may have technical applications to probe the two-body Coulomb interaction.

Non-Markovian full counting statistics in quantum dot molecules

Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules.

Gigahertz single-trap electron pumps in silicon

Manipulation of single electrons is the key to developing ultimate electronics such as single-electron-based information processors and electrical standards in metrology. Especially, high-frequency and high-accuracy single-electron pumps are essential to realize practical current standards. While electrically defined quantum dots are widely used to build single-electron pumps, a localized state in semiconductors is also a potential candidate for accurate pumps because it can have a large activation energy for the captured electron. However, the transfer mechanism of such localized-state-mediated single-electron pumps for high-accuracy operation at a high frequency has not been well examined. Here we demonstrate a single-electron pump using a single-trap level with an activation energy of a few ten millielectron volts in Si nanotransistors. By means of gate control of capture and emission rates, the pump operates at a frequency of 3 GHz with an accuracy of better than 10(-3) at 17 K, indicating that an electric field at the trap level lowers the capture and emission time to less than 25 ps.

Self-referenced single-electron quantized current source

The future redefinition of the international system of units in terms of natural constants requires a robust, high-precision quantum standard for the electrical base unit ampere. However, the reliability of any single-electron current source generating a nominally quantized output current I=ef by delivering single electrons with charge e at a frequency f is eventually limited by the stochastic nature of the underlying quantum mechanical tunneling process. We experimentally explore a path to overcome this fundamental limitation by serially connecting clocked single-electron emitters with multiple in situ single-electron detectors. Correlation analysis of the detector signatures during current generation reveals erroneous pumping events and enables us to determine the deviation of the output current from the nominal quantized value ef. This demonstrates the concept of a self-referenced single-electron source for electrical quantum metrology.

A charge parity ammeter

A metallic double dot is measured with radio frequency reflectometry. Changes in the total electron number of the double dot are determined via single electron tunnelling contributions to the complex electrical impedance. Electron counting experiments are performed by monitoring the impedance, demonstrating operation of a single electron ammeter without the need for external charge detection.