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 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...

Theory of the electron spin relaxation in graphene on the SiO2 substrate is developed. Charged impurities and polar optical surface phonons in the substrate induce an effective random BychkovRashba-like spin-orbit coupling field which leads to spin relaxation by the D'yakonov-Perel' mechanism. Analytical estimates and Monte Carlo simulations show that the corresponding spin relaxation times are between micro-to milliseconds, being only weakly temperature dependent. It is also argued that the presence of adatoms on graphene can lead to spin lifetimes shorter than nanoseconds.PACS numbers: 72.25. Rb, 73.61.Wp, 73.50.Bk Since the experimental realization of graphene, a single stable 2D-monolayer of carbon atoms arranged in a honeycomb lattice, considerable research has been done to enlighten its peculiar electronic transport properties originating from the Dirac-like band structure at the K and K ′ points in the momentum space [1]. Long spin relaxation times and phase coherence lengths in graphene are expected based on the weak atomic spin-orbit coupling in carbon (Z = 6). However, recent spin injection measurements based on a non-local spin valve geometry [2, 3, 4] revealed surprisingly short spin relaxation times of only about 100-200 ps, being only weakly dependent on the charge density and temperature. These results appear puzzling, although the low mobilities of the samples (about 2000 cm 2 /Vs) suggest that the measured spin relaxation times are likely due to extrinsic effects [2].Very recent experiments on the charge transport in graphene affirmed the importance of the underlying substrate [5,6,7]. At low temperatures the transport properties have been shown to be dominated by scattering from the charged impurities residing in the substrate [6,8]. The conductivity of graphene placed on a SiO 2 substrate starts to decrease above 200 K. The observed temperature and density dependence of the resistivity are most likely explained by remote phonon scattering due to occurrence of polar optical surface modes in the substrate [9, 10, 11].These findings naturally raise the question if (i) charged impurities and (ii) remote surface phonons are also relevant for the spin relaxation in graphene. As argued here both mechanisms provide a temperaturedependent, random spin-orbit coupling field, which limits the spin relaxation via the D'yakonov-Perel' (DP) mechanism [12,13,14]. The calculated spin relaxation times are micro to milliseconds. In addition, we give estimates for the spin relaxation times due to the possible presence of adatoms on graphene. For reasonable adatom densities the spin lifetimes can be lower than nanoseconds.Several other mechanisms have already been investigated theoretically, such as the spin relaxation due to the corrugations (ripples) of graphene and due to exchange interaction with local magnetic moments [15], or spin-

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We investigate surface plasmons at a planar interface between a normal dielectric and a topological insulator, where the Fermi-energy lies inside the bulk gap of the topological insulator and gives rise to a two-dimensional charge distribution of free Dirac electrons. We develop the methodology for the calculation of plasmon dispersions, using the framework of classical electrodynamics, with modified constituent equations due to Hall currents in the topological insulator, together with a Lindhard-type description for the two-dimensional charge distribution of free Dirac electrons. For a system representative for Bi$_2$X$_3$ binary compounds, we find in agreement with recent related work that the modified constituent equations have practically no impact on the surface plasmon dispersion but lead to a rotation of the magnetic polarization of surface plasmons out of the interface plane.Comment: 5 pages, 2 figure