Few-electron Quantum Dots Research Articles

Tunable p–n junction barriers in few-electron bilayer graphene quantum dots

Graphene quantum dots provide promising platforms for hosting spin, valley, or spin-valley qubits. Taking advantage of their electrically generated bandgap and their ambipolar nature, high-quality quantum dots can be defined in bilayer graphene using natural p–n junctions as tunnel barriers. In these devices, demonstrating the electrical tunability of the p–n junction barriers and understanding its physical mechanism, especially in the few-electron regime, are essential for further manipulating electrons' quantum degrees of freedom to encode qubits. Here, we show the electrostatic confinement of single quantum dots in bilayer graphene using natural p–n junctions. When the device is operated in the few-electron regime, the electron tunneling rate is found to be monotonically tuned by varying gate voltages, which can be well understood from the view of manipulating the p–n junction barriers. Our results provide an insightful understanding of electrostatic confinement using natural p–n junctions in bilayer graphene, which is beneficial for realizing graphene-based qubits.

Electron g-factor determined for quantum dot circuit fabricated from (110)-oriented GaAs quantum well

The choice of substrate orientation for semiconductor quantum dot circuits offers opportunities for tailoring spintronic properties such as g-factors for specific functionality. Here, we demonstrate the operation of a few-electron double quantum dot circuit fabricated from a (110)-oriented GaAs quantum well. We estimate the in-plane electron g-factor from the profile of the enhanced inter-dot tunneling (leakage) current near-zero magnetic field. Spin blockade due to Pauli exclusion can block inter-dot tunneling. However, this blockade becomes inactive due to hyperfine interaction mediated spin flip-flop processes between electron spin states and the nuclear spin of the host material. The g-factor of absolute value ∼0.1 found for a magnetic field parallel to the direction [1¯10] is approximately a factor of four lower than that for comparable circuits fabricated from a material grown on widely employed standard (001) GaAs substrates and is in line with reported values determined by purely optical means for quantum well structures grown on (110) GaAs substrates.

Tunneling theory for a bilayer graphene quantum dot’s single- and two-electron states

The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot states’ orbital, spin, and valley composition from differential conductance in a finite magnetic field. Furthermore, we show that the transport features manifest splittings in the dot’s spin and valley multiplets induced by interactions and magnetic field (the latter splittings being a consequence of bilayer graphene’s Berry curvature). Our results elucidate spin- and valley-dependent tunnelling mechanisms and will help to utilize bilayer graphene quantum dots, e.g., as spin and valley qubits.

Growth of PbTe nanowires by molecular beam epitaxy

Advances in quantum technology may come from the discovery of new materials systems that improve the performance or allow for new functionality in electronic devices. Lead telluride (PbTe) is a member of the group IV–VI materials family that has significant untapped potential for exploration. Due to its high electron mobility, strong spin–orbit coupling and ultrahigh dielectric constant it can host few-electron quantum dots and ballistic quantum wires with opportunities for control of electron spins and other quantum degrees of freedom. Here, we report the fabrication of PbTe nanowires by molecular beam epitaxy. We achieve defect-free single crystalline PbTe with large aspect ratios up to 50 suitable for quantum devices. Furthermore, by fabricating a single nanowire field effect transistor, we attain bipolar transport, extract the bandgap and observe Fabry–Pérot oscillations of conductance, a signature of quasiballistic transmission.

Shell Filling and Trigonal Warping in Graphene Quantum Dots

Transport measurements through a few-electron circular quantum dot in bilayer graphene display bunching of the conductance resonances in groups of four, eight, and twelve. This is in accordance with the spin and valley degeneracies in bilayer graphene and an additional threefold "minivalley degeneracy" caused by trigonal warping. For small electron numbers, implying a small dot size and a small displacement field, a two-dimensional s shell and then a p shell are successively filled with four and eight electrons, respectively. For electron numbers larger than 12, as the dot size and the displacement field increase, the single-particle ground state evolves into a threefold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in the magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.

Real-Time Feedback Control of Charge Sensing for Quantum Dot Qubits

Measurement of charge configurations in few-electron quantum dots is a vital technique for spin-based quantum information processing. While fast and high-fidelity measurement is possible by using proximal quantum dot charge sensors, their operating range is limited and prone to electrical disturbances. Here we demonstrate realtime operation of a charge sensor in a feedback loop to maintain its sensitivity suitable for fast charge sensing in a Si/SiGe double quantum dot. Disturbances to the charge sensitivity, due to variation of gate voltages for operating the quantum dot and $1/f$ charge fluctuation, are compensated by a digital PID controller with the bandwidth of $\approx 100\,{\rm kHz}$. The rapid automated tuning of a charge sensor enables unobstructed charge stability diagram measurement facilitating realtime quantum dot tuning and submicrosecond single-shot spin readout without compromising the performance of a charge sensor in time-consuming experiments for quantum information processing.

Tunable interdot coupling in few-electron bilayer graphene double quantum dots

We present a highly controllable double quantum dot device based on bilayer graphene. Using a device architecture of interdigitated gate fingers, we can control the interdot tunnel coupling between 1 and 4 GHz and the mutual capacitive coupling between 0.2 and 0.6 meV, independent of the charge occupation of the quantum dots. The charging energy and, hence, the dot size remain nearly unchanged. The tuning range of the tunnel coupling covers the operating regime of typical silicon and GaAs spin qubit devices.

Dispersive sensing of charge states in a bilayer graphene quantum dot

We demonstrate dispersive readout of individual charge states in a gate-defined few-electron quantum dot in bilayer graphene. We employ a radio frequency reflectometry circuit, where an LC resonator with a resonance frequency close to 280 MHz is directly coupled to an Ohmic contact of the quantum dot device. The detection scheme based on changes in the quantum capacitance operates over a wide gate-voltage range and allows us to probe excited states down to the single-electron regime. Crucially, the presented sensing technique avoids the use of an additional, capacitively coupled quantum device such as a quantum point contact or single electron transistor, making dispersive sensing particularly interesting for gate-defined graphene quantum dots.

Measurements of anisotropic g-factors for electrons in InSb nanowire quantum dots

We have measured the Zeeman splitting of quantum levels in few-electron quantum dots (QDs) formed in narrow bandgap InSb nanowires via the Schottky barriers at the contacts under application of different spatially orientated magnetic fields. The effective g-factor tensor extracted from the measurements is strongly anisotropic and level-dependent, which can be attributed to the presence of strong spin–orbit interaction (SOI) and asymmetric quantum confinement potentials in the QDs. We have demonstrated a successful determination of the principal values and the principal axis orientations of the g-factor tensors in an InSb nanowire QD by the measurements under rotations of a magnetic field in the three orthogonal planes. We also examine the magnetic field evolution of the excitation spectra in an InSb nanowire QD and extract a SOI strength of ∼ 180 μeV from an avoided level crossing between a ground state and its neighboring first excited state in the QD.

Characterizing Quantum Devices at Scale with Custom Cryo-CMOS

We make use of a custom-designed cryo-CMOS multiplexer to enable multiple quantum devices to be characterized in a single cooldown of a dilution refrigerator. Combined with a packaging approach that integrates cryo-CMOS chips and a hot-swappable parallel-device test platform, we describe how this setup takes the standard wiring configuration of a dilution refrigerator as input and expands the capability for batch characterization of quantum devices at milli-Kelvin temperatures and high magnetic fields. The architecture of the cryo-CMOS multiplexer is discussed, and its performance is benchmarked using few-electron quantum dots and Hall mobility mapping measurements.

Path-integral Monte Carlo study of electronic states in quantum dots in an external magnetic field

We explore the correlated electron states in harmonically confined few-electron quantum dots in an external magnetic field by the path-integral Monte Carlo method for a wide range of the field and the Coulomb interaction strength. Using the phase structure of a preceding unrestricted Hartree-Fock calculation for phase fixing, we find a rich variety of correlated states, often completely different from the prediction of mean-field theory. These are finite temperature results, but sometimes the correlations saturate with decreasing temperature, providing insight into the ground-state properties.

Andreev bound states in a few-electron quantum dot coupled to superconductors

A direct measurement of the density of Andreev bound states (ABSs) is experimentally investigated in a superconductor--quantum dot--superconductor hybrid nanowire system. A hard proximity-induced superconducting gap is observed, arising from superconducting correlations, in the transport spectrum of the hybrid system. Conductance peaks observed inside the superconducting gap reveal that the subgap states participate in the transport of the hybrid junction. We explore the evolution of low-energy Andreev bound states in a few-electron quantum dot (QD) coupled to superconductors, by probing the magnetic field dependence of exquisite detailed conductance spectra with a small bias voltage applied on the superconducting lead. In the presence of low magnetic fields, the resonance current is enhanced and broadened, attributed to the transport through Andreev bound states in QD, as the energy of ABSs reaches the threshold set by the applied bias voltage with the increase of the magnetic field. The simulated transport spectrum matches the experimentally observed evolution patterns of conductance, further implying the superconducting correlation nature of the observed electron transport. At high magnetic fields, the conductance maxes as the Fermi level reaches the degeneration point of Landau levels, leading to conductance peaks shown in the alternating narrow and wide patterns of Coulomb blockade oscillations.

Negative exchange interactions in coupled few-electron quantum dots

It has been experimentally shown that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here, we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons.

Single-electron Spin Resonance in a Quadruple Quantum Dot.

Electron spins in semiconductor quantum dots are good candidates of quantum bits for quantum information processing. Basic operations of the qubit have been realized in recent years: initialization, manipulation of single spins, two qubit entanglement operations, and readout. Now it becomes crucial to demonstrate scalability of this architecture by conducting spin operations on a scaled up system. Here, we demonstrate single-electron spin resonance in a quadruple quantum dot. A few-electron quadruple quantum dot is formed within a magnetic field gradient created by a micro-magnet. We oscillate the wave functions of the electrons in the quantum dots by applying microwave voltages and this induces electron spin resonance. The resonance energies of the four quantum dots are slightly different because of the stray field created by the micro-magnet and therefore frequency-resolved addressable control of each electron spin resonance is possible.

Topological Phase and Half-Integer Orbital Angular Momenta in Circular Quantum Dots

We show that there exists a non-trivial topological phase in circular two-dimensional quantum dots with an odd number of electrons. The possible non-zero value of this phase is explained by axial symmetry of two-dimensional quantum systems. The particular value of this phase ( $$\pi $$ ) is fixed by T-invariance and the Pauli exclusion principle and leads to half-integer values of the angular orbital momentum for ground states of such systems. This conclusion agrees with the experimental data for ground-state energies of few-electron circular quantum dots in perpendicular magnetic field (Schmidt et al. in Phys Rev B 51:5570, 1995). Hence, these data may be considered as the first experimental evidence for the existence of topological phase leading to half-integer quantization of the orbital angular momentum in circular quantum dots with an odd number of electrons.

Magnetotransport studies of mobility limiting mechanisms in undoped Si/SiGe heterostructures

We perform detailed magnetotransport studies on two-dimensional electron gases (2DEGs) formed in undoped Si/SiGe heterostructures in order to identify the electron mobility limiting mechanisms in this increasingly important materials system. By analyzing data from 26 wafers with different heterostructure growth profiles we observe a strong correlation between the background oxygen concentration in the Si quantum well and the maximum mobility. The highest quality wafer supports a 2DEG with a mobility of 160,000 cm^2/Vs at a density 2.17 x 10^11/cm^2 and exhibits a metal-to-insulator transition at a critical density 0.46 x 10^11/cm^2. We extract a valley splitting of approximately 150 microeV at a magnetic field of 1.8 T. These results provide evidence that undoped Si/SiGe heterostructures are suitable for the fabrication of few-electron quantum dots.

A reconfigurable gate architecture for Si/SiGe quantum dots

We demonstrate a reconfigurable quantum dot gate architecture that incorporates two interchangeable transport channels. One channel is used to form quantum dots, and the other is used for charge sensing. The quantum dot transport channel can support either a single or a double quantum dot. We demonstrate few-electron occupation in a single quantum dot and extract charging energies as large as 6.6 meV. Magnetospectroscopy is used to measure valley splittings in the range of 35–70 μeV. By energizing two additional gates, we form a few-electron double quantum dot and demonstrate tunable tunnel coupling at the (1,0) to (0,1) interdot charge transition.

Validity of the single-particle description and charge noise resilience for multielectron quantum dots

We construct an optimal set of single-particle states for few-electron quantum dots (QDs) using the method of natural orbitals (NOs). The NOs include also the effects of the Coulomb repulsion between electrons. We find that they agree well with the noniteracting orbitals for GaAs QDs of realistic parameters, while the Coulomb interactions only rescale the radius of the NOs compared to the noninteracting case. We use NOs to show that four-electron QDs are less susceptible to charge noise than their two-electron counterparts.

Lithographically defined few-electron silicon quantum dots based on a silicon-on-insulator substrate

Silicon quantum dot (QD) devices with a proximal single-electron transistor (SET) charge sensor have been fabricated in a metal-oxide-semiconductor structure based on a silicon-on-insulator substrate. The charge state of the QDs was clearly read out using the charge sensor via the SET current. The lithographically defined small QDs enabled clear observation of the few-electron regime of a single QD and a double QD by charge sensing. Tunnel coupling on tunnel barriers of the QDs can be controlled by tuning the top-gate voltages, which can be used for manipulation of the spin quantum bit via exchange interaction between tunnel-coupled QDs. The lithographically defined silicon QD device reported here is technologically simple and does not require electrical gates to create QD confinement potentials, which is advantageous for the integration of complicated constructs such as multiple QD structures with SET charge sensors for the purpose of spin-based quantum computing.

Single-electron shell occupation and effectivegfactor in few-electron nanowire quantum dots

Nanowire double quantum dots occupied by an even number of electrons are investigated in the context of energy level structure revealed by electric dipole spin resonance measurements. We use numerically exact configuration interaction approach up to 6 electrons for systems tuned to Pauli spin blockade regime. We point out the differences between the spectra of systems with two and a greater number of electrons. For two-electrons the unequal length of the dots results in a different effective $g$-factors in the dots as observed by the recent experiments. For an increased number of electrons the $g$-factor difference between the dots appears already for symmetric systems and it is greatly amplified when the dots are of unequal length. We find that in the lowest energy states all except of two electrons form a frozen core of singlet shells that can be separated away for description of the properties of the system.