Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as Non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the ν = 5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the ν = 5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

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. CONTENTS

We propose and analyze theoretically an experimental setup for detecting the elusive Majorana particle in semiconductor-superconductor heterostructures. The experimental system consists of one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded into a superconducting quantum interference device. We show that the energy spectra of the Andreev bound states at the junction are qualitatively different in topologically trivial (i.e., not containing any Majorana) and nontrivial phases having an even and odd number of crossings at zero energy, respectively. The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage. The observation of this phase transition will be a direct demonstration of the existence of Majorana particles.

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We show that a film of a semiconductor in which s-wave superconductivity and Zeeman splitting are induced by the proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. Since time-reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose-a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator-is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.

The dynamical dielectric function of two dimensional graphene at arbitrary wave vector q and frequency ω, ǫ(q, ω), is calculated in the self-consistent field approximation. The results are used to find the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in 2D graphene layer within the random phase approximation. At long wavelengths (q → 0) the plasmon dispersion shows the local classical behavior ω cl = ω0 √ q, but the density dependence of the plasma frequency (ω0 ∝ n 1/4 ) is different from the usual 2D electron system (ω0 ∝ n 1/2 ). The wave vector dependent plasmon dispersion and the static screening function show very different behavior than the usual 2D case. We show that the intrinsic interband contributions to static graphene screening can be effectively absorbed in a background dielectric constant.

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities nimp. For dirty samples (250 ؋ 10 10 cm ؊2 < nimp < 400 ؋ 10 10 cm ؊2 ), the value of the minimum conductivity at low carrier density is indeed 4e 2 /h in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on nimp, increasing to 8e 2 /h for nimp Ϸ 20 ؋ 10 10 cm ؊2 . A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.Boltzmann transport ͉ electron transport ͉ minimum conductivity

Carrier transport in gated 2D graphene monolayers is theoretically considered in the presence of scattering by random charged impurity centers with density ni. Excellent quantitative agreement is obtained (for carrier density n > 10 12 cm −2 ) with existing experimental data (Ref. 1, 2, 3, 4, 5). The conductivity scales linearly with n/ni in the theory, and shows extremely weak temperature dependence. The experimentally observed asymmetry between electron and hole conductivities is explained by the asymmetry in the charged impurity configuration in the presence of the gate voltage, while the high-density saturation of conductivity for the highest mobility samples is explained as a crossover between the long-range and the point scattering dominated regimes. We argue that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for n ni ∼ 10 12 cm −2 .