Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

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Spintronics: Fundamentals and applications

Department of Materials Science, University of Patras, 26504 Rio Patras, Greece, Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vass. Constantinou Avenue, 116 35 Athens, Greece, Institut de Biologie Moleculaire et Cellulaire, UPR9021 CNRS, Immunologie et Chimie Therapeutiques, 67084 Strasbourg, France, and Dipartimento di Scienze Farmaceutiche, Universita di Trieste, Piazzale Europa 1, 34127 Trieste, Italy

Chemistry of Carbon Nanotubes

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.

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Spins in few-electron quantum dots

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future

Quantum Computing

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-not. We then describe the single-qubit Hadamard, Ŝ and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of Appendices in which we provide supplementary information to the main text. © 2012 American Physical Society.

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Surface codes: Towards practical large-scale quantum computation

A quantum-dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to the presence of level crossings where the qubit becomes chargelike. Here, we show how to exploit the level crossings to implement fast pulsed gating. We develop one- and two-qubit dc quantum gates that are simpler than the previously proposed ac gates. We obtain closed-form solutions for the control sequences and show that the gates are fast (subnanosecond) and can achieve high fidelities.

Pulse-gated quantum-dot hybrid qubit.

We report integrated charge sensing measurements on a Si/SiGe double quantum dot. The quantum dot is shown to be tunable from a single, large dot to a well-isolated double dot. Charge sensing measurements enable the extraction of the tunnel coupling t between the quantum dots as a function of the voltage on the top gates defining the device. Control of the voltage on a single such gate tunes the barrier separating the two dots. The measured tunnel coupling is an exponential function of the gate voltage. The ability to control t is an important step toward controlling spin qubits in silicon quantum dots.

Charge sensing and controllable tunnel coupling in a Si/SiGe double quantum dot.

We have fabricated scanning probe microscope cantilevers with dimensions 65×11.4×0.25 μm3 and 3×2×0.129 μm3 from GaAs/Al0.3Ga0.7As heterostructures containing two-dimensional electron gases. Deflection is measured by an integrated field-effect transistor (FET) that senses strain via the piezoelectric effect and provides a low noise, low power displacement readout. We present images of a 200 nm mica grating taken with the large cantilever having a deflection (force) noise 10 A/√Hz (19 pN/√Hz) at T=2.2 K. The small cantilever has a resonant frequency of 11 MHz, a FET gate charge noise of 0.001 e/√Hz, and is projected to have a deflection (force) noise of 0.002 A/√Hz (1 pN/√Hz) at T=4.2 K.

GaAs/AlGaAs self-sensing cantilevers for low temperature scanning probe microscopy

The authors investigate the magnetic field dependence of the energy splitting between low-lying valley states for electrons in a Si∕SiGe quantum well tilted with respect to the crystallographic axis. The presence of atomic steps at the quantum well interface may explain the unexpected, strong suppression of the valley splitting observed in recent experiments. The authors find that the suppression is caused by an interference effect associated with multiple steps, and that the magnetic field dependence arises from the lateral confinement of the electronic wave function. Using numerical simulations, the authors clarify the role of step disorder, obtaining quantitative agreement with the experiments.

Magnetic field dependence of valley splitting in realistic Si∕SiGe quantum wells

Single-electron occupation is an essential component to the measurement and manipulation of spin in quantum dots, capabilities that are important for quantum information processing. Si∕SiGe is of interest for semiconductor spin qubits, but single-electron quantum dots have not yet been achieved in this system. We report the fabrication and measurement of a top-gated quantum dot occupied by a single electron in a Si∕SiGe heterostructure. Transport through the quantum dot is directly correlated with charge sensing from an integrated quantum point contact, and this charge sensing is used to confirm single-electron occupancy in the quantum dot.

Mark A. Eriksson

Papers

Pulse-gated quantum-dot hybrid qubit.

Charge sensing and controllable tunnel coupling in a Si/SiGe double quantum dot.

GaAs/AlGaAs self-sensing cantilevers for low temperature scanning probe microscopy

Magnetic field dependence of valley splitting in realistic Si∕SiGe quantum wells

Single-electron quantum dot in Si∕SiGe with integrated charge sensing