There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

The appealing electronic properties of the monolayer semiconductor molybdenum disulphide make it a candidate material for electronic devices. The observation of tightly bound trions in this system—which have no analogue in conventional semiconductors—opens up possibilities for controlling these quasiparticles in future optoelectronic applications.

Tightly bound trions in monolayer MoS2

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

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New directions in the pursuit of Majorana fermions in solid state systems.

We have confirmed that a spin-orbit interaction in an inverted I${\mathrm{n}}_{0.53}$G${\mathrm{a}}_{0.47}$As/I${\mathrm{n}}_{0.52}$A${\mathrm{l}}_{0.48}$As quantum well can be controlled by applying a gate voltage. This result shows that the spin-orbit interaction of a two-dimensional electron gas depends on the surface electric field. The dominant mechanism for the change in the spin-orbit interaction parameter can be attributed to the Rashba term. This inverted I${\mathrm{n}}_{0.53}$G${\mathrm{a}}_{0.47}$As/I${\mathrm{n}}_{0.52}$A${\mathrm{l}}_{0.48}$As heterostructure is one of the promising materials for the spin-polarized field effect transistor which is proposed by Datta and Das [Appl. Phys. Lett. 56, 665 (1990)].

Gate Control of Spin-Orbit Interaction in an Inverted I n 0.53 G a 0.47 As/I n 0.52 A l 0.48 As Heterostructure

We have investigated the values of the Rashba spin-orbit coupling constant alpha in In(0.52)Al(0.48)As/In(0.53)Ga(0.47)As/In(0.52)Al(0.48)As quantum wells using the weak antilocalization (WAL) analysis as a function of the structural inversion asymmetry (SIA) of the quantum wells. We have found that the deduced alpha values have a strong correlation with the degree of SIA of the quantum wells as predicted theoretically. The good agreement between the theoretical and experimental values of alpha suggests that our WAL approach for deducing alpha values provides a useful tool in designing future spintronics devices that utilize the Rashba spin-orbit coupling.

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Rashba spin-orbit coupling probed by the weak antilocalization analysis in InAlAs/InGaAs/InAlAs quantum wells as a function of quantum well asymmetry.

A gated inverted ${\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.53}{\mathrm{Ga}}_{0.47}{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ quantum well is studied via magnetotransport. By analyzing the gate-voltage-dependent beating pattern observed in the Shubnikov--de Haas oscillation, we determine the gate voltage (or electron concentration) dependence of the spin-orbit coupling parameter \ensuremath{\alpha}. Our experimental data and its analysis show that the band nonparabolicity effect cannot be neglected. For electron concentrations above $2\ifmmode\times\else\texttimes\fi{}{10}^{12}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2},$ it causes a reduction of \ensuremath{\alpha} up to 25%. We report the \ensuremath{\alpha} value for the second subband.

Zero-field spin splitting in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure: Band nonparabolicity influence and the subband dependence

We have confirmed the quantization of the critical current in a superconducting quantum point contact consisting of a split-gate superconductor-(two-dimensional electron gas)-superconductor junction. The critical current and conductance show stepwise changes as a function of the gate voltage. We also observed resonant structure resulting from quantum interference of quasiparticles at the step edge.

Observation of maximum supercurrent quantization in a superconducting quantum point contact

A Josephson field effect transistor (JOFET) was coupled with a two‐dimensional electron gas in a strained InAs quantum well inserted into an In0.52Al0.48As/In0.53Ga0.47As inverted modulation‐doped structure. The characteristics of this JOFET are much improved over previous devices by using a high electron mobility transistor (HEMT)‐type gate instead of the usual metal‐insulator‐ semiconductor (MIS)‐type gate. The superconducting critical current as well as the junction normal resistance are completely controlled via a gate voltage of about −1 V; this provides voltage gain over 1 for a JOFET.

Tatsushi Akazaki

Papers

Gate Control of Spin-Orbit Interaction in an Inverted I n 0.53 G a 0.47 As/I n 0.52 A l 0.48 As Heterostructure

Rashba spin-orbit coupling probed by the weak antilocalization analysis in InAlAs/InGaAs/InAlAs quantum wells as a function of quantum well asymmetry.

Zero-field spin splitting in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure: Band nonparabolicity influence and the subband dependence

Observation of maximum supercurrent quantization in a superconducting quantum point contact

A Josephson field effect transistor using an InAs‐inserted‐channel In0.52Al0.48As/In0.53Ga0.47As inverted modulation‐doped structure