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

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry-giant magnetoresistance systems are used as hard disk read heads-semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spindependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field. 72.25.Rb, 75.50.Pp, PACS

The isolation of graphene has triggered an avalanche of studies into the spin-dependent physical properties of this material and of graphene-based spintronic devices. Here, we review the experimental and theoretical state-of-art concerning spin injection and transport, defect-induced magnetic moments, spin-orbit coupling and spin relaxation in graphene. Future research in graphene spintronics will need to address the development of applications such as spin transistors and spin logic devices, as well as exotic physical properties including topological states and proximity-induced phenomena in graphene and other two-dimensional materials.

We present k· p Hamiltonians parametrised by ab initio density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the K, Q, Γ, and M points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides. We discuss the parametrisation of the essential parts of the k· p Hamiltonians for MoS 2 , MoSe 2 , MoTe 2 , WS 2 , WSe 2 , and WTe 2 , including the spin-splitting and spin-polarisation of the bands, and we briefly review the vibrational properties of these materials. We then use k· p theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualisation of scanning tunnelling microscopy maps. PACS numbers:Contents 1 Introduction 2 2 Lattice parameters, band-structure calculations and vibrational properties 43 Band-edge energy differences and spin-splittings 7 4 Valence band width D vb 9 arXiv:1410.6666v3 [cond-mat.mes-hall] 6 Apr 2015 k · p theory for 2D TMDCs to be studied without constructing slabs in three-dimensionally periodic cells and the resulting electronic spectra are free of plane-wave continua. All our fleur calculations were carried out with a cut-off k max of 10.6 eV −1 for the plane-wave basis set and 144 k points corresponding to a 12 × 12 × 1 Monkhorst-Pack grid in the irreducible wedge of the BZ. Muffin-tin radii of 1.0, 1.21, 1.27, 1.27, and 1.27Å were used for S, Se, Te, Mo, and W, respectively. We note that considering local orbitals for Mo (s, p), Se (s, p, d), and W (s, p, f ) to improve the linearised augmented plane-wave basis proved to be crucial for a correct description of the excited states. We used the Perdew-Burke-Ernzerhof (PBE) generalised gradient approximation [83] to the exchange-correlation potential. The structures were relaxed (with the effects of SOC included) until the forces were less than 0.0005 eV/Å. The calculated values of a 0 and d S−S for monolayer TMDCs are shown in Table 1 and compared to measured values for the corresponding bulk materials. The lattice parameters obtained from the first of the DFT approaches described above are shown in the rows labelled by "(HSE)", the ones from the second approach are in the rows labelled by "(PBE)". "(Exp)" indicates experimental results found in the literature. Although there is some scatter in the experimental data, Table 1 suggests that using the HSE06 functional to relax the monolayer crystal structure leads to a good agreement with the room-temperature empirical bulk a 0 values. On the other hand, the PBE functional seems to slightly overestimates a 0 . However, the situation is less clear in the case of d X−X . We note that both the HSE06 and the PBE results are in good agreement with Reference [84].Recent experiments show that the energy of the photoluminescence peak is quite sensitive to the temperature [5,85,86], which can be understood in terms of th...

The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap of 24 eV ͑0.28 K͒ at the K͑KЈ͒ point. It is shown that the previously accepted value of 1 eV, coming from the -mixing, is incorrect due to the neglect of d and higher orbitals whose contribution is dominant due to symmetry reasons. The transverse electric field induces an additional ͑extrinsic͒ Bychkov-Rashba-type splitting of 10 eV ͑0.11 K͒ per V/nm, coming from the -mixing. A "miniripple" configuration with every other atom shifted out of the sheet by less than 1% differs little from the intrinsic case.The fascination with graphene, 1 the one-atom-thick allotrope of carbon, comes from its two-dimensional structure as well as from its unique electronic properties. 2-7 The latter originate from the specific electronic band structure at the Fermi level: electrons move with a constant velocity, apparently without mass and a spectral gap. Analogy with massless Dirac fermions is often drawn, presenting graphene as a solid-state toy for relativistic quantum mechanics. Ironically, this nice analogy is broken by the relativistic effects themselves. In particular, the interaction of the orbital and spin degrees of freedom, spin-orbit coupling, gives the electrons in graphene a finite mass and induces a gap in the spectrum. How large is the gap and which orbital states contribute to it? This question is crucial for knowing graphene's bandstructure topology, understanding its spin transport and spin relaxation properties, 8,9 or for assessing prospects of graphene for spin-based quantum computing. 10 By performing comprehensive first principles calculations we predict the spectral gap and establish the relevant electronic spectrum of graphene in the presence of external transverse electric field. We find that realistic electric fields can tune among different band structure topologies with important ramifications for the physics of graphene.Carbon atoms in graphene are arranged in a honeycomb lattice which comprises two triangular Bravais lattices; the unit cell has two atoms. The corresponding reciprocal lattice is again honeycomb, with two nonequivalent vertices K and KЈ which are the Fermi momenta of a neutral graphene. The states relevant for transport are concentrated in two touching cones with the tips at K͑KЈ͒-the Dirac points-as illustrated in Fig. 1. The corresponding Bloch states are formed mainly by the carbon valence p z orbitals ͑the z axis is perpendicular to the graphene plane͒ forming the two bands ͑cones͒. The other three occupied valence states of carbon form the deep-lying bands by sp 2 hybridization; these are responsible for the robustness of graphene's structure. The states in the lower cones are holelike or valencelike, while the upper cone states are electronlike or conductionlike, borrowing from semiconductor terminology. These essentials of the electronic band struct...

No abstract

The spin-orbit coupling in graphene induces spectral gaps at the high-symmetry points. The relevant gap at the ⌫ point is similar to the splitting of the p orbitals in the carbon atom, being roughly 8.5 meV. The splitting at the K point is orders of magnitude smaller. Earlier tight-binding theories indicated the value of this intrinsic gap of 1 eV, based on the -coupling. All-electron first-principles calculations give much higher values, between 25 and 50 eV, due to the presence of the orbitals of the d symmetry in the Bloch states at K. A realistic multiband tight-binding model is presented to explain the effects the d orbitals play in the spin-orbit coupling at K. The -coupling is found irrelevant to the value of the intrinsic spin-orbit-induced gap. On the other hand, the extrinsic spin-orbit coupling ͑of the Bychkov-Rashba type͒, appearing in the presence of a transverse electric field, is dominated by the -hybridization, in agreement with previous theories. Tightbinding parameters are obtained by fitting to first-principles calculations, which also provide qualitative support for the model when considering the trends in the spin-orbit-induced gap in graphene under strain. Finally, an effective single-orbital next-nearest-neighbor hopping model accounting for the spin-orbit effects is derived.

Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs for sulfides and selenides, while it merges with the valence band for tellurides. In the former case, the proximity-induced staggered potential gaps and spin-orbit couplings (all on the meV scale) of the Dirac electrons are established by fitting to a phenomenological effective Hamiltonian. While graphene on MoS 2 , MoSe 2 , and WS 2 has a topologically trivial band structure, graphene on WSe 2 exhibits inverted bands. Using a realistic tight-binding model we find topologically protected helical edge states for graphene zigzag nanoribbons on WSe 2 , demonstrating the quantum spin Hall effect. This model also features "half-topological states," which are protected against time-reversal disorder on one edge only.