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

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

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Berry phase effects on electronic properties

Materials research plays a vital role in transforming breakthrough scientific ideas into next-generation technology. Similar to the way silicon revolutionized the microelectronics industry, the proper materials can greatly impact the field of plasmonics and metamaterials. Currently, research in plasmonics and metamaterials lacks good material building blocks in order to realize useful devices. Such devices suffer from many drawbacks arising from the undesirable properties of their material building blocks, especially metals. There are many materials, other than conventional metallic components such as gold and silver, that exhibit metallic properties and provide advantages in device performance, design flexibility, fabrication, integration, and tunability. This review explores different material classes for plasmonic and metamaterial applications, such as conventional semiconductors, transparent conducting oxides, perovskite oxides, metal nitrides, silicides, germanides, and 2D materials such as graphene. This review provides a summary of the recent developments in the search for better plasmonic materials and an outlook of further research directions.

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Alternative Plasmonic Materials: Beyond Gold and Silver

The observation of oscillations in the conductance characteristics of narrow graphene p–n-junctions confirms their ability to collimate ballistic carriers. Moreover, the phase of these oscillations at low magnetic field suggests the occurrence of the perfect transmission of carriers normal to the junction as a direct result of the Klein effect. The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality1,2,3,4. Although electron optics such as lensing5 and focusing6 have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge owing to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength7. Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resonant cavity is formed between two electrostatically created bipolar junctions. Analysis of the oscillations confirms that p–n junctions have a collimating effect on ballistically transmitted carriers8. The phase shift observed in the conductance fringes at low magnetic fields is a signature of the perfect transmission of carriers normally incident on the junctions9 and thus constitutes a direct experimental observation of ‘Klein tunnelling’10,11,12.

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Quantum interference and Klein tunnelling in graphene heterojunctions

I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

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Quantum Transport in Semiconductor Nanostructures

Oscillations in the surface structure of Sn-doped GaAs during growth by MBE

Transverse electron focusing in a two-dimensional electron gas is investigated experimentally and theoretically for the first time. A split Schottky gate on top of a GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructure defines two point contacts of variable width, which are used as injector and collector of ballistic electrons. As evidenced by their quantized conductance, these are quantum point contacts with a width comparable to the Fermi wavelength. At low magnetic fields, skipping orbits at the electron-gas boundary are directly observed, thereby establishing that boundary scattering is highly specular. Large additional oscillatory structure in the focusing spectra is observed at low temperatures and for small point-contact size. This new phenomenon is interpreted in terms of interference of coherently excited magnetic edge states in a two-dimensional electron gas. A theory for this effect is given, and the relation with nonlocal resistance measurements in quantum ballistic transport is discussed. It is pointed out, and experimentally demonstrated, that four-terminal transport measurements in the electron-focusing geometry constitute a determination of either a generalized longitudinal resistance or a Hall resistance. At high magnetic fields the electron-focusing peaks are suppressed, and a transition is observed to the quantum Hall regime. The anomalous quantum Hall effect in this geometry is discussed in light of a four-terminal resistance formula.

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Coherent electron focusing with quantum point contacts in a two-dimensional electron gas

We have studied the electron transport in a one-dimensional electron interferometer. It consists of a disk-shaped two-dimensional electron gas, to which quantum point contacts are attached. Discrete zero-dimensional states are formed due to constructive interference of electron waves traveling along the circumference of the disk in one-dimensional magnetic edge channels. The conductance shows pronounced Aharonov-Bohm–type oscillations, with maxima occurring whenever the energy of a zero-dimensional state coincides with the Fermi energy. Good agreement with theory is found, taking energy averaging into account.

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Observation of zero-dimensional states in a one-dimensional electron interferometer.

The two-terminal conductance of ballistic point contacts in the two-dimensional electron gas of a high-mobility $\frac{\mathrm{GaAs}}{{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}}$ heterostructure has been studied in quantizing electric and magnetic fields. The conductance is found to be quantized at multiples of $\frac{{e}^{2}}{h}$, exclusively determined by the number of occupied magnetoelectric subbands in the constriction. The experiment provides the first direct demonstration of magnetic and electric depopulation of one-dimensional subbands in a single wire.

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Quantized conductance of magnetoelectric subbands in ballistic point contacts

We report a definitive optical detection, using band-gap photoluminescence, of the integer and fractional quantum Hall effects in GaAs by a comprehensive study of integer states from \ensuremath{\nu}=1 to 10 and the \ensuremath{\nu}=2/3 hierarchy out to the 5/9 daughter state, in an ultrahigh-mobility single heterojunction at 120 mK.

J.J. Harris

Papers

Oscillations in the surface structure of Sn-doped GaAs during growth by MBE

Coherent electron focusing with quantum point contacts in a two-dimensional electron gas

Observation of zero-dimensional states in a one-dimensional electron interferometer.

Quantized conductance of magnetoelectric subbands in ballistic point contacts

Optical detection of the integer and fractional quantum Hall effects in GaAs.