S. Tarucha

Spins in few-electron quantum dots

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

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.

Few-electron quantum dots

We review some electron transport experiments on few-electron, vertical quantum dot devices. The measurement of current versus source–drain voltage and gate voltage is used as a spectroscopic tool to investigate the energy characteristics of interacting electrons confined to a small region in a semiconducting material. Three energy scales are distinguished: the single-particle states, which are discrete due to the confinement involved; the direct Coulomb interaction between electron charges on the dot; and the exchange interaction between electrons with parallel spins. To disentangle these energies, a magnetic field is used to reorganize the occupation of electrons over the single-particle states and to induce changes in the spin states. We discuss the interactions between small numbers of electrons (between 1 and 20) using the simplest possible models. Nevertheless, these models consistently describe a large set of experiments. Some of the observations resemble similar phenomena in atomic physics, such as shell structure and periodic table characteristics, Hund’s rule, and spin singlet and triplet states. The experimental control, however, is much larger than for atoms: with one device all the artificial elements can be studied by adding electrons to the quantum dot when changing the gate voltage.

Trilayer graphene is a semimetal with a gate-tunable band overlap

Graphene-based materials are promising candidates for nanoelectronic devices because very high carrier mobilities can be achieved without the use of sophisticated material preparation techniques. However, the carrier mobilities reported for single-layer and bilayer graphene are still less than those reported for graphite crystals at low temperatures, and the optimum number of graphene layers for any given application is currently unclear, because the charge transport properties of samples containing three or more graphene layers have not yet been investigated systematically. Here, we study charge transport through trilayer graphene as a function of carrier density, temperature, and perpendicular electric field. We find that trilayer graphene is a semimetal with a resistivity that decreases with increasing electric field, a behaviour that is markedly different from that of single-layer and bilayer graphene. We show that the phenomenon originates from an overlap between the conduction and valence bands that can be controlled by an electric field, a property that had never previously been observed in any other semimetal. We also determine the effective mass of the charge carriers, and show that it accounts for a large part of the variation in the carrier mobility as the number of layers in the sample is varied.

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.

Electrically driven single-electron spin resonance in a slanting Zeeman field

The integration of a micrometre-sized magnet with a semiconductor device has enabled the individual manipulation of two single electron spins. This approach may provide a scalable route for quantum computing with electron spins confined in quantum dots.

Allowed and forbidden transitions in artificial hydrogen and helium atoms

The strength of radiative transitions in atoms is governed by selection rules that depend on the occupation of atomic orbitals with electrons. Experiments have shown similar electron occupation of the quantized energy levels in semiconductor quantum dots—often described as artificial atoms. But unlike real atoms, the confinement potential of quantum dots is anisotropic, and the electrons can easily couple with phonons of the material. Here we report electrical pump-and-probe experiments that probe the allowed and ‘forbidden’ transitions between energy levels under phonon emission in quantum dots with one or two electrons (artificial hydrogen and helium atoms). The forbidden transitions are in fact allowed by higher-order processes where electrons flip their spin. We find that the relaxation time is about 200 µs for forbidden transitions, 4 to 5 orders of magnitude longer than for allowed transitions. This indicates that the spin degree of freedom is well separated from the orbital degree of freedom, and that the total spin in the quantum dots is an excellent quantum number. This is an encouraging result for potential applications of quantum dots as basic entities for spin-based quantum information storage.

Contact resistance in graphene-based devices

We report a systematic study of the total contact resistance present at the interface between a metal (Ti) and graphene layers of different, known thickness. By comparing devices fabricated on many different graphene flakes we demonstrate that the contact resistance consists of a gate independent and a gate dependent part. We show that quantitatively the gate independent part of the contact resistance is the same for single-, bi-, and tri-layer graphene. We argue that this is the result of charge transfer from the metal, causing the Fermi level in the graphene region under the contacts to shift far away from the charge neutrality point.

Tuneable electronic properties in graphene

Novel materials are in great demand for future applications. The discovery of graphene, a one atom thick carbon layer, holds the promise for unique device architectures and functionalities exploiting unprecedented physical phenomena. The ability to embed graphene materials in a double gated structure allowed on-chip realization of relativistic tunneling experiments in single layer graphene, the discovery of a gate tunable band gap in bilayer graphene and of a gate tunable band overlap in trilayer graphene. Here we discuss recent advances in the physics and nanotechnology fabrication of double gated single- and few-layer graphene devices.