Charge localization and reentrant superconductivity in a quasi-ballistic InAs nanowire coupled to superconductors.

A semiconductor nanowire with strong spin-orbit coupling in proximity to a superconductor is predicted to display Majorana edge states emerging under a properly oriented magnetic field. The experimental investigation of these exotic states requires assessing the one-dimensional (1D) character of the nanowire and understanding the superconducting proximity effect in the presence of a magnetic field. Here, we explore the quasi-ballistic 1D transport regime of an InAs nanowire with Ta contacts. Fine-tuned by means of local gates, the observed plateaus of approximately quantized conductance hide the presence of a localized electron, giving rise to a lurking Coulomb blockade effect and Kondo physics. When Ta becomes superconducting, this local charge causes an unusual, reentrant magnetic field dependence of the supercurrent, which we ascribe to a 0 - π transition. Our results underline the relevant role of unintentional charge localization in the few-channel regime where helical subbands and Majorana quasi-particles are expected to arise.

Gate-reflectometry dispersive readout and coherent control of a spin qubit in silicon.

Silicon spin qubits have emerged as a promising path to large-scale quantum processors. In this prospect, the development of scalable qubit readout schemes involving a minimal device overhead is a compelling step. Here we report the implementation of gate-coupled rf reflectometry for the dispersive readout of a fully functional spin qubit device. We use a p-type double-gate transistor made using industry-standard silicon technology. The first gate confines a hole quantum dot encoding the spin qubit, the second one a helper dot enabling readout. The qubit state is measured through the phase response of a lumped-element resonator to spin-selective interdot tunneling. The demonstrated qubit readout scheme requires no coupling to a Fermi reservoir, thereby offering a compact and potentially scalable solution whose operation may be extended above 1 K.

Ballistic One-Dimensional Holes with Strong g-Factor Anisotropy in Germanium.

We report experimental evidence of ballistic hole transport in one-dimensional quantum wires gate-defined in a strained SiGe/Ge/SiGe quantum well. At zero magnetic field, we observe conductance plateaus at integer multiples of 2 e2/ h. At finite magnetic field, the splitting of these plateaus by Zeeman effect reveals largely anisotropic g-factors with absolute values below 1 in the quantum-well plane, and exceeding 10 out-of-plane. This g-factor anisotropy is consistent with a heavy-hole character of the propagating valence-band states, which is in line with a predominant confinement in the growth direction. Remarkably, we observe quantized ballistic conductance in device channels up to 600 nm long. These findings mark an important step toward the realization of novel devices for applications in quantum spintronics.

A CMOS silicon spin qubit.

Silicon, the main constituent of microprocessor chips, is emerging as a promising material for the realization of future quantum processors. Leveraging its well-established complementary metal-oxide-semiconductor (CMOS) technology would be a clear asset to the development of scalable quantum computing architectures and to their co-integration with classical control hardware. Here we report a silicon quantum bit (qubit) device made with an industry-standard fabrication process. The device consists of a two-gate, p-type transistor with an undoped channel. At low temperature, the first gate defines a quantum dot encoding a hole spin qubit, the second one a quantum dot used for the qubit read-out. All electrical, two-axis control of the spin qubit is achieved by applying a phase-tunable microwave modulation to the first gate. The demonstrated qubit functionality in a basic transistor-like device constitutes a promising step towards the elaboration of scalable spin qubit geometries in a readily exploitable CMOS platform.

Electrical Control of g-Factor in a Few-Hole Silicon Nanowire MOSFET.

Hole spins in silicon represent a promising yet barely explored direction for solid-state quantum computation, possibly combining long spin coherence, resulting from a reduced hyperfine interaction, and fast electrically driven qubit manipulation. Here we show that a silicon-nanowire field-effect transistor based on state-of-the-art silicon-on-insulator technology can be operated as a few-hole quantum dot. A detailed magnetotransport study of the first accessible hole reveals a g-factor with unexpectedly strong anisotropy and gate dependence. We infer that these two characteristics could enable an electrically driven g-tensor-modulation spin resonance with Rabi frequencies exceeding several hundred mega-Hertz.

The coupled atom transistor.

We describe the first implementation of a coupled atom transistor where two shallow donors (P or As) are implanted in a nanoscale silicon nanowire and their electronic levels are controlled with three gate voltages. Transport spectroscopy through these donors placed in series is performed both at zero and microwave frequencies. The coherence of the charge transfer between the two donors is probed by Landau-Zener-Stückelberg interferometry. Single-charge transfer at zero bias (electron pumping) has been performed and the crossover between the adiabatic and non-adiabatic regimes is studied.

Coherent coupling of two dopants in a silicon nanowire probed by Landau-Zener-Stückelberg interferometry.

We report on microwave-driven coherent electron transfer between two coupled donors embedded in a silicon nanowire. By increasing the microwave frequency we observe a transition from incoherent to coherent driving revealed by the emergence of a Landau-Zener-Stückelberg quantum interference pattern of the measured current through the donors. This interference pattern is fitted to extract characteristic parameters of the double-donor system. In particular we estimate a charge dephasing time of 0.3±0.1 ns, comparable to other types of charge-based two-level systems. The demonstrated coherent coupling between two dopants is an important step towards donor-based quantum computing devices in silicon.

Nature of tunable hole g factors in quantum dots.

We report an electric-field-induced giant modulation of the hole g factor in SiGe nanocrystals. The observed effect is ascribed to a so-far overlooked contribution to the g factor that stems from the mixing between heavy- and light-hole wave functions. We show that the relative displacement between the confined heavy- and light-hole states, occurring upon application of the electric field, alters their mixing strength leading to a strong nonmonotonic modulation of the g factor.

Monolithic growth of ultrathin Ge nanowires on Si(001).

Self-assembled Ge wires with a height of only 3 unit cells and a length of up to 2 micrometers were grown on Si(001) by means of a catalyst-free method based on molecular beam epitaxy. The wires grow horizontally along either the [100] or the [010] direction. On atomically flat surfaces, they exhibit a highly uniform, triangular cross section. A simple thermodynamic model accounts for the existence of a preferential base width for longitudinal expansion, in quantitative agreement with the experimental findings. Despite the absence of intentional doping, the first transistor-type devices made from single wires show low-resistive electrical contacts and single-hole transport at sub-Kelvin temperatures. In view of their exceptionally small and self-defined cross section, these Ge wires hold promise for the realization of hole systems with exotic properties and provide a new development route for silicon-based nanoelectronics.

Observation of spin-selective tunneling in SiGe nanocrystals.

Spin-selective tunneling of holes in SiGe nanocrystals contacted by normal-metal leads is reported. The spin selectivity arises from an interplay of the orbital effect of the magnetic field with the strong spin-orbit interaction present in the valence band of the semiconductor. We demonstrate both experimentally and theoretically that spin-selective tunneling in semiconductor nanostructures can be achieved without the use of ferromagnetic contacts. The reported effect, which relies on mixing the light and heavy holes, should be observable in a broad class of quantum-dot systems formed in semiconductors with a degenerate valence band.

Quantum transport in GaN/AlN double-barrier heterostructure nanowires.

We investigate electronic transport in n-i-n GaN nanowires with and without AlN double barriers. The nanowires are grown by catalyst-free, plasma-assisted molecular beam epitaxy enabling abrupt GaN/AlN interfaces as well as longitudinal n-type doping modulation. At low temperature, transport in n-i-n GaN nanowires is dominated by the Coulomb blockade effect. Carriers are confined in the undoped middle region, forming single or multiple islands with a characteristic length of approximately 100 nm. The incorporation of two AlN tunnel barriers causes confinement to occur within the GaN dot in between. In the case of a 6 nm thick dot and 2 nm thick barriers, we observe characteristic signatures of Coulomb-blockaded transport in single quantum dots with discrete energy states. For thinner dots and barriers, Coulomb-blockade effects do not play a significant role while the onset of resonant tunneling via the confined quantum levels is accompanied by a negative differential resistance surviving up to approximately 150 K.

Hybrid superconductor-semiconductor devices made from self-assembled SiGe nanocrystals on silicon.

The epitaxial growth of germanium on silicon leads to the self-assembly of SiGe nanocrystals by a process that allows the size, composition and position of the nanocrystals to be controlled. This level of control, combined with an inherent compatibility with silicon technology, could prove useful in nanoelectronic applications. Here, we report the confinement of holes in quantum-dot devices made by directly contacting individual SiGe nanocrystals with aluminium electrodes, and the production of hybrid superconductor-semiconductor devices, such as resonant supercurrent transistors, when the quantum dot is strongly coupled to the electrodes. Charge transport measurements on weakly coupled quantum dots reveal discrete energy spectra, with the confined hole states displaying anisotropic gyromagnetic factors and strong spin-orbit coupling with pronounced dependences on gate voltage and magnetic field.

Electronic transport spectroscopy of carbon nanotubes in a magnetic field.

We report magnetic field spectroscopy measurements in carbon nanotube quantum dots exhibiting fourfold shell structure in the energy level spectrum. The magnetic field induces a large splitting between the two orbital states of each shell, demonstrating their opposite magnetic moment and determining transitions in the spin and orbital configuration of the quantum dot ground state. We use inelastic cotunneling spectroscopy to accurately resolve the spin and orbital contributions to the magnetic moment. A small coupling is found between orbitals with opposite magnetic moment leading to anticrossing behavior at zero field.

Magnetically induced chessboard pattern in the conductance of a Kondo quantum dot.

We quantitatively describe the main features of the magnetically induced conductance modulation of a Kondo quantum dot-or chessboard pattern-in terms of a constant-interaction double quantum dot model. We show that the analogy with a double dot holds down to remarkably low magnetic fields. The analysis is extended by full 3D spin density functional calculations. Introducing an effective Kondo coupling parameter, the chessboard pattern is self-consistently computed as a function of magnetic field and electron number, which enables us to explain our experimental data quantitatively.

Out-of-equilibrium Kondo effect in a mesoscopic device.

We study the nonequilibrium regime of the Kondo effect in a quantum dot laterally coupled to a narrow wire. We observe a split Kondo resonance when a finite bias voltage is imposed across the wire. The splitting is attributed to the creation of a double-step Fermi distribution function in the wire. Kondo correlations are strongly suppressed when the voltage across the wire exceeds the Kondo temperature. A perpendicular magnetic field enables us to selectively control the coupling between the dot and the two Fermi seas in the wire. Already at fields of order 0.1 T only the Kondo resonance associated with the strongly coupled reservoir survives.

Two-stage Kondo effect in a quantum dot at a high magnetic field.

We report a strong Kondo effect (Kondo temperature approximately 4 K) at high magnetic field in a selective area growth semiconductor quantum dot. The Kondo effect is ascribed to a singlet-triplet transition in the ground state of the dot. At the transition, the low-temperature conductance approaches the unitary limit. Away from the transition, for low bias voltages and temperatures, the conductance is sharply reduced. The observed behavior is compared to predictions for a two-stage Kondo effect in quantum dots coupled to single-channel leads.

Electron cotunneling in a semiconductor quantum dot.

We report transport measurements on a semiconductor quantum dot with a small number of confined electrons. In the Coulomb blockade regime, conduction is dominated by cotunneling processes. These can be either elastic or inelastic, depending on whether they leave the dot in its ground state or drive it into an excited state, respectively. We are able to discriminate between these two contributions and show that inelastic events can occur only if the applied bias exceeds the lowest excitation energy. Implications to energy-level spectroscopy are discussed.

The kondo effect in the unitary limit

We observe a strong Kondo effect in a semiconductor quantum dot when a small magnetic field is applied. The Coulomb blockade for electron tunneling is overcome completely by the Kondo effect, and the conductance reaches the unitary limit value. We compare the experimental Kondo temperature with the theoretical predictions for the spin- 12 Anderson impurity model. Excellent agreement is found throughout the Kondo regime. Phase coherence is preserved when a Kondo quantum dot is included in one of the arms of an Aharonov-Bohm ring structure, and the phase behavior differs from previous results on a non-Kondo dot.

Kondo effect in an integer-spin quantum dot

The Kondo effect--a many-body phenomenon in condensed-matter physics involving the interaction between a localized spin and free electrons--was discovered in metals containing small amounts of magnetic impurities, although it is now recognized to be of fundamental importance in a wide class of correlated electron systems. In fabricated structures, the control of single, localized spins is of technological relevance for nanoscale electronics. Experiments have already demonstrated artificial realizations of isolated magnetic impurities at metallic surfaces, nanoscale magnets, controlled transitions between two-electron singlet and triplet states, and a tunable Kondo effect in semiconductor quantum dots. Here we report an unexpected Kondo effect in a few-electron quantum dot containing singlet and triplet spin states, whose energy difference can be tuned with a magnetic field. We observe the effect for an even number of electrons, when the singlet and triplet states are degenerate. The characteristic energy scale is much larger than in the ordinary spin-1/2 case.