Few-electron Quantum Dots Research Articles

Thermopower of few-electron quantum dots with Kondo correlations

The thermopower of few-electron quantum dots is crucially influenced by on-dot electron-electron interactions, particularly in the presence of Kondo correlations. In this paper, we present a comprehensive picture which elucidates the underlying relations between the thermopower and the spectral density function of two-level quantum dots. The effects of various electronic states, including the Kondo states originating from both spin and orbital degrees of freedom, are clearly unraveled. Such a physical picture is affirmed by accurate numerical data obtained with a hierarchical equations of motion approach. Our findings and understandings provide an effective and viable way to control the thermoelectric properties of strongly correlated quantum dot systems.

Quantum computer aided design simulation and optimization of semiconductor quantum dots

We present the Quantum Computer Aided Design (QCAD) simulator that targets modeling multi-dimensional quantum devices, particularly silicon multi-quantum dots (QDs) developed for quantum bits (qubits). This finite-element simulator has three differentiating features: (i) its core contains nonlinear Poisson, effective mass Schrodinger, and Configuration Interaction solvers that have massively parallel capability for high simulation throughput and can be run individually or combined self-consistently for 1D/2D/3D quantum devices; (ii) the core solvers show superior convergence even at near-zero-Kelvin temperatures, which is critical for modeling quantum computing devices; and (iii) it interfaces directly with the full-featured optimization engine Dakota. In this work, we describe the capabilities and implementation of the QCAD simulation tool and show how it can be used to both analyze existing experimental QD devices through capacitance calculations and aid in the design of few-electron multi-QDs. In particular, we observe that computed capacitances are in rough agreement with experiment, and that quantum confinement increases capacitance when the number of electrons is fixed in a quantum dot. Coupling of QCAD with the optimizer Dakota allows for rapid identification and improvement of device layouts that are likely to exhibit few-electron quantum dot characteristics.

Coulomb interaction and valley-orbit coupling in Si quantum dots

The valley-orbit coupling in a few-electron Si quantum dot is expected to be a function of its occupation number $N$. We study the spectrum of multivalley Si quantum dots for $2\ensuremath{\le}N\ensuremath{\le}4$, showing that, counterintuitively, electron-electron interaction effects on the valley-orbit coupling are negligible. For $N=2$ they are suppressed by valley interference, for $N=3$ they vanish due to spinor overlaps, and for $N=4$ they cancel between different pairs of electrons. To corroborate our theoretical findings, we examine the experimental energy spectrum of a few-electron metal-oxide-semiconductor quantum dot. The measured spin-valley state filling sequence in a magnetic field reveals that the valley-orbit coupling is definitively unaffected by the occupation number.

Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by the scanning probe technique

We perform a numerical simulation of the mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps as a function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are compared with the original ones. This study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limiting case. We concentrate on large quantum dots for which strong electron–electron correlations appear. For circular dots the correlations lead to the formation of Wigner molecules that in the presence of a tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for a repulsive tip potential and overestimated for an attractive tip. In lower symmetry quantum dots Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of a tip. These charge densities are well resolved by the mapping. These single-electron islands appear in the laboratory frame provided that the classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.

Electron Dynamics of Interatomic Coulombic Decay in Quantum Dots: Singlet Initial State

In this paper we investigated the interatomic Coulombic decay (ICD) of a resonance singlet state in a model potential for two few-electron semiconductor quantum dots (QDs) by means of electron dynamics. We demonstrate that ICD is the major decay process of the resonance for the singlet wave function and compare the total and partial decay widths as a function of the QD separation with that from our previous study on the corresponding triplet states [1].

Hund’s rule in the two-electron quantum dot

Hund’s rule, specifying that in an open shell configuration the state of higher total spin has a lower energy, is also applicable to few-electron quantum dots. However, the relative contributions of the different energetic components behave in a qualitatively distinct way. This is accounted for by application of the virial theorem.

Orbital and valley state spectra of a few-electron silicon quantum dot

Understanding interactions between orbital and valley quantum states in silicon nanodevices is crucial in assessing the prospects of spin-based qubits. We study the energy spectra of a few-electron silicon metal-oxide-semiconductor quantum dot using dynamic charge sensing and pulsed-voltage spectroscopy. The occupancy of the quantum dot is probed down to the single-electron level using a nearby single-electron transistor as a charge sensor. The energy of the first orbital excited state is found to decrease rapidly as the electron occupancy increases from N=1 to 4. By monitoring the sequential spin filling of the dot we extract a valley splitting of ~230 {\mu}eV, irrespective of electron number. This indicates that favorable conditions for qubit operation are in place in the few-electron regime.

A few-electron quadruple quantum dot in a closed loop

We report the realization of a quadruple quantum dot device in a square-like configuration where a single electron can be transferred on a closed path free of other electrons. By studying the stability diagrams of this system, we demonstrate that we are able to reach the few-electron regime and to control the electronic population of each quantum dot with gate voltages. This allows us to control the transfer of a single electron on a closed path inside the quadruple dot system. This work opens the route towards electron spin manipulation using spin-orbit interaction by moving an electron on complex paths free of electrons.

Electrostatic Spin Control in InAs/InP Nanowire Quantum Dots

Very robust voltage-controlled spin transitions in few-electron quantum dots are demonstrated. Two lateral-gate electrodes patterned on opposite sides of an InAs/InP nanowire are used to apply a transverse electric field and tune orbital energy separation down to level-pair degeneracy. Transport measurements in this regime allow us to demonstrate the breakdown of the standard alternate up/down spin filling scheme and unambiguously show singlet-triplet spin transitions. The strong confinement of the present devices leads to a large energy gain for the observed anomalous spin configurations that exceeds 4 meV. As a consequence, this behavior is well visible even at temperatures exceeding T = 20 K.

Spin-orbit interaction induced singlet-triplet resonant Raman transitions in quantum dot helium

From our theoretical studies of resonant Raman transitions in two-electron quantum dots (artificial helium atoms) we show that in this system, the singlet-triplet Raman transitions are allowed (in polarized configuration) only in the presence of spin-orbit interactions. With an increase of the applied magnetic field this transition dominates over the singlet-singlet and triplet-triplet transitions. This intriguing effect can therefore be utilized to tune Raman transitions as well as the spin-orbit coupling in few-electron quantum dots.

Fabrication and characterization of a silicon metal-oxide-semiconductor based triple quantum dot

We fabricate electrostatically defined, few-electron triple quantum dot (TQD) devices in a silicon metal-oxide-semiconductor structure and obtain stability diagrams in the few-electron regime through charge detection by a nearby quantum point contact. We demonstrate the tunability of the TQD by achieving the quadruple points where all three dots are on resonance. The tuning evolutions are shown to be consistent with a constant interaction model. We identify quantum cellular automata phenomena near the quadruple point.

Charge dynamics of a single donor coupled to a few-electron quantum dot in silicon

We report on the charge transfer dynamics between a silicon quantum dot and an individual phosphorous donor extracted from the current through the quantum dot as a probe for the donor ionization state. We employ a silicon n-metal-oxide-semiconductor field-effect transistor (MOSFET) with two side gates at a single metallization level to control both the device conductance and the donor charge. The elastic nature of the process is demonstrated by temperature and magnetic field independent tunneling times. The Fano factor approaches 1/2 revealing that the process is sub-poissonian.

Resonance-hybrid states in a triple quantum dot

Delocalization by resonance between contributing structures explains the enhanced stability of resonance-hybrid molecules. Here we report the realization of resonance-hybrid states in a few-electron triple quantum dot (TQD) obseved by excitation spectroscopy. The stabilization of the resonance-hybrid state and the bond between contributing states are achieved through access to the intermediate states with double occupancy of the dots. This explains why the energy of the hybridized singlet state is significantly lower than that of the triplet state. The properties of the three-electron doublet states can also be understood with the resonance-hybrid picture and geometrical phase. As well as for fundamental TQD physics, our results are useful for the investigation of materials such as quantum dot arrays, quantum information processors, and chemical reaction and quantum simulators.

First-principles study of electron transport in few-electron open quantum dots by the Hartree–Fock approach

Electron transport properties of few-electron open quantum dots within the spin-restricted Hartree–Fock approximation are studied. The self-consistent numerical calculations were performed for a whole device, including the semi-infinite leads, without employing any phenomenological or adjustable parameters. Inclusion of the non-local Fock potential brings qualitatively new physics in comparison to the Hartree approach: electron screening decreases, resonant energy levels become less pinned to the Fermi energy and clearly correlate with conductance peaks. When coupling between the dot and leads decreases the number of electrons inside the dot becomes quantized and the model predicts the Coulomb blockade of electron transport. This is confirmed by comparison with the master equation approach for an equivalent quantum dot.

Magnetic phase diagram of non-magnetic few-electron quantum dot molecules

A pathway to design non-magnetic artificial molecules which display controllable magnetic properties is addressed theoretically by studying the effects of in-plane electrical field, spin–orbit interaction (SOI) and geometrical parameters on the magnetic phase transitions in few-electron lateral double quantum dots (DQDs). We demonstrate the tunability of the magnetic phase diagram of two-electron DQDs as the system is changed from a molecule to an atom, in both weak and strong SOI regimes. We find an unusual jump in the magnetization and an asymmetric peak of the magnetic susceptibility. In addition, both the asymmetric susceptibility peak position and the magnetic phase diagram are strongly dependent on the interdot tunnel coupling, which can be tuned effectively by changing repulsive barrier voltage and/or interdot distance, the number of electrons and the SOI strength. With increasing interdot tunnel-coupling strength, for instance, the rate of paramagnetic-to-diamagnetic phase area increases. The SOI makes the paramagnetic phase more stable under magnetic field. Moreover, the effects of geometry deviation on the electronic structure and magnetic property of the DQD are also discussed.

Determination of energy scales in few-electron double quantum dots

The capacitive couplings between gate-defined quantum dots and their gates vary considerably as a function of applied gate voltages. The conversion between gate voltages and the relevant energy scales is usually performed in a regime of rather symmetric dot-lead tunnel couplings strong enough to allow direct transport measurements. Unfortunately, this standard procedure fails for weak and possibly asymmetric tunnel couplings, often the case in realistic devices. We have developed methods to determine the gate voltage to energy conversion accurately in the different regimes of dot-lead tunnel couplings and demonstrate strong variations of the conversion factors. Our concepts can easily be extended to triple quantum dots or even larger arrays.

Mechanically probing coherent tunneling in a double quantum dot

We study theoretically the interaction between the charge dynamics of a few-electron double quantum dot and a capacitively-coupled AFM cantilever, a setup realized in several recent experiments. We demonstrate that the dot-induced frequency shift and damping of the cantilever can be used as a sensitive probe of coherent inter-dot tunnelling, and that these effects can be used to quantitatively extract both the magnitude of the coherent interdot tunneling and (in some cases) the value of the double-dot T_1 time. We also show how the adiabatic modulation of the double-dot eigenstates by the cantilever motion leads to new effects compared to the single-dot case.

Dynamically controlled charge sensing of a few-electron silicon quantum dot

We report charge sensing measurements of a silicon metal-oxide-semiconductor quantum dot using a single-electron transistor as a charge sensor with dynamic feedback control. Using digitally-controlled feedback, the sensor exhibits sensitive and robust detection of the charge state of the quantum dot, even in the presence of charge drifts and random charge upset events. The sensor enables the occupancy of the quantum dot to be probed down to the single electron level.

Non-equilibrium charge stability diagrams of a silicon double quantum dot

We report on the experimental characterization of an electrostatically defined, few-electron double quantum dot in a silicon metal-oxide-semiconductor (MOS) structure. The device incorporates two quasi-one-dimensional channels for sensing the charge states of the double quantum dot. Charge sensor stability diagrams obtained at finite source-drain bias are interpreted and used to find the absolute energy scale of the quantum dots based on a matrix representation of the coupling between the dots and the gates.

Single-shot measurement and tunnel-rate spectroscopy of a Si/SiGe few-electron quantum dot

We investigate the tunnel rates and energies of excited states of small numbers of electrons in a quantum dot fabricated in a Si/SiGe heterostructure. Tunnel rates for loading and unloading electrons are found to be strongly energy dependent, and they vary significantly between different excited states. We show that this phenomenon enables charge sensing measurements of the average electron occupation that are analogous to Coulomb diamonds. Excited-state energies can be read directly from the plot, and we develop a rate model that enables a quantitative understanding of the relative sizes of different electron tunnel rates.