S. De Franceschi

Electron transport through double quantum dots

Electron transport experiments on two lateral quantum dots coupled in series are reviewed. An introduction to the charge stability diagram is given in terms of the electrochemical potentials of both dots. Resonant tunneling experiments show that the double dot geometry allows for an accurate determination of the intrinsic lifetime of discrete energy states in quantum dots. The evolution of discrete energy levels in magnetic field is studied. The resolution allows one to resolve avoided crossings in the spectrum of a quantum dot. With microwave spectroscopy it is possible to probe the transition from ionic bonding (for weak interdot tunnel coupling) to covalent bonding (for strong interdot tunnel coupling) in a double dot artificial molecule. This review is motivated by the relevance of double quantum dot studies for realizing solid state quantum bits.

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.

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.

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.

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.

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.

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.

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.

Quantum Computing with Electron Spins in Quantum Dots

We present a set of concrete and realistic ideas for the implementation of a small-scale quantum computer using electron spins in lateral GaAs/AlGaAs quantum dots. Initialization is based on leads in the quantum Hall regime with tunable spin-polarization. Readout hinges on spin- to-charge conversion via spin-selective tunneling to or from the leads, followed by measurement of the number of electron charges on the dot via a charge detector. Single-qubit manipulation relies on a microfabricated wire located close to the quantum dot, and two-qubit interactions arc controlled via the tunnel barrier connecting the respective quantum dots. Based on these ideas, we have begun a series of experiments in order to demonstrate unitary control and to measure the coherence time of individual electron spins in quantum dots.