A. H. MacDonald

Anomalous Hall effect

We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE together with the more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Finally we discuss outstanding issues and avenues for future investigation.

Universal Intrinsic Spin Hall Effect

We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.

Theory of ferromagnetic (III,Mn)V semiconductors

The body of research on (III,Mn)V diluted magnetic semiconductors initiated during the 1990s has concentrated on three major fronts: i) the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, ii) the materials science of growth and defects and iii) the development of spintronic devices with new functionalities. This article reviews the current status of the field, concentrating on the first two, more mature research directions. From the fundamental point of view, (Ga,Mn)As and several other (III,Mn)V DMSs are now regarded as textbook examples of a rare class of robust ferromagnets with dilute magnetic moments coupled by delocalized charge carriers. Both local moments and itinerant holes are provided by Mn, which makes the systems particularly favorable for realizing this unusual ordered state. Advances in growth and post-growth treatment techniques have played a central role in the field, often pushing the limits of dilute Mn moment densities and the uniformity and purity of materials far beyond those allowed by equilibrium thermodynamics. In (III,Mn)V compounds, material quality and magnetic properties are intimately connected. In the review we focus on the theoretical understanding of the origins of ferromagnetism and basic structural, magnetic, magneto-transport, and magneto-optical characteristics of simple (III,Mn)V epilayers, with the main emphasis on (Ga,Mn)As. The conclusions we arrive at are based on an extensive literature covering results of complementary ab initio and effective Hamiltonian computational techniques, and on comparisons between theory and experiment.

Graphene: Exploring carbon flatland

Just one atom thick, this two-dimensional semiconductor does not resemble any known material.

Photonic topological insulators

We review the recent progress on the first experimental demonstration of photonic topological insulators, along with a variety of new ideas associated with it.Recent progress in understanding the topological pr operties of condensed matter has led to the discove ry of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologi cally non-trivial electronic order seems to be uncommon e xcept in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show t ha artificial electromagnetic structures, known as metamaterials, provide an attractive platform for d esigning photonic analogues of topological insulato rs. We demonstrate that a judicious choice of the metam a erial parameters can create photonic phases that support a pair of helical edge states, and that the se edge states enable one-way photonic transport th at is robust against disorder.

Intrinsic and Rashba spin-orbit interactions in graphene sheets

Starting from a microscopic tight-binding model and using second-order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength

Spintronics and pseudospintronics in graphene and topological insulators

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Ferromagnetic semiconductors: moving beyond (Ga,Mn)As

and first order in the external electric field

Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

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Quantum transport of massless Dirac fermions.

perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at