This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.

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Electronic transport in two-dimensional graphene

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 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 nteraction 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 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

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Semiconductor Spintronics

This article reviews the theoretical and experimental work related to the electronic properties of bilayer graphene systems. Three types of bilayer stackings are discussed: the AA, AB, and twisted bilayer graphene. This review covers single-electron properties, effects of static electric and magnetic fields, bilayer-based mesoscopic systems, spin-orbit coupling, dc transport and optical response, as well as spontaneous symmetry violation and other interaction effects. The selection of the material aims to introduce the reader to the most commonly studied topics of theoretical and experimental research in bilayer graphene.

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Electronic properties of graphene-based bilayer systems

Spin waves constitute an important part of research in the field of magnetization dynamics. Spin waves are the elementary excitations of the spin system in a magnetically ordered material state and magnons are their quasi particles. In the following article, we will discuss the optical method of Brillouin light scattering (BLS) spectroscopy which is a now a well established tool for the characterization of spin waves. BLS is the inelastic scattering of light from spin waves and confers several benefits: the ability to map the spin wave intensity distribution with spatial resolution and high sensitivity as well as the potential to simultaneously measure the frequency and the wave vector and, therefore, the dispersion properties. For several decades, the field of spin waves gained huge interest by the scientific community due to its relevance regarding fundamental issues of spindynamics in the field of solid states physics. The ongoing research in recent years has put emphasis on the high potential of spin waves regarding information technology. In the emerging field of \textit{magnonics}, several concepts for a spin-wave based logic have been proposed and realized. Opposed to charge-based schemes in conventional electronics and spintronics, magnons are charge-free currents of angular momentum, and, therefore, less subject to scattering processes that lead to heating and dissipation. This fact is highlighted by the possibility to utilize spin waves as information carriers in electrically insulating materials. These developments have propelled the quest for ways and mechanisms to guide and manipulate spin-wave transport. In particular, a lot of effort is put into the miniaturization of spin-wave waveguides and the excitation of spin waves in structures with sub-micrometer dimensions. For the further development of potential spin-wave-based devices, the ability to directly observe spin-wave propagation with spatial resolution is crucial. As an optical technique BLS do

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Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale

We have observed collective spin-wave modes in inhomogeneously magnetized ${\mathrm{Ni}}_{081}{\mathrm{Fe}}_{019}$ thin-film stripes The stripes, 18 nm thick and $2\ensuremath{\mu}\mathrm{m}$ wide, are studied in an in-plane magnetic field oriented along their short axes When the magnetic field is on the order of the shape anisotropy field, the equilibrium magnetization near the stripe edges rotates 90 deg over a length scale of order $100\mathrm{nm}--1\ensuremath{\mu}\mathrm{m}$ Time-resolved Kerr microscopy is used to detect a hierarchy of spin-wave modes in these edge regions Using a combination of semianalytical theory and micromagnetic simulations, we show that these modes span the entire stripe but can only be detected near the edges, where the effective wave vector is small

Spin waves in an inhomogeneously magnetized stripe

We report on the study of the fractional quantum Hall effect at the filling factor 5/2 using exact diagonalization method with torus geometry. The particle-hole symmetry breaking effect is considered using an additional three-body interaction. Both Pfaffian and anti-Pfaffian states can be the ground state depending on the sign of the three-body interaction. The results of the low-energy spectrum, the wave function overlap, and the particle-hole parity evolution, have shown clear evidence of a direct sharp transition (possibly first order) from the Pfaffian to the anti-Pfaffian state at the Coulomb point. A quantum phase diagram is established, where one finds further transitions from the Pfaffian or anti-Pfaffian state to the nearby compressible phases induced by a change of the pseudopotential.

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Particle-hole symmetry breaking and the ν= 5 2 fractional quantum Hall effect

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [Phys. Rev. Lett. 107, 116801 (2011)].

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Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

We investigate spin-dependent transport through a band-gap-matched ZnSe/Zn1−xMnxSe heterostructure with a single paramagnetic layer under influence of both an electric and a magnetic field. It is shown that the magnetic-field tunable potential and its symmetry in this system can be significantly modulated by the electric field, which results in obvious dependence of the magnitude of the electronic spin polarization on the electric field magnitude. The results obtained in this work might shed light on the development of new electron-polarized devices.

Spin-polarized transport through a ZnSe/Zn1−xMnxSe heterostructure under an applied electric field

We investigate spin-polarized transport through semimagnetic semiconductor heterostructures under the influence of both an external electric field and a magnetic field. The structural symmetric and asymmetric effects as well as the electric-field effect are stressed. The results indicate that (1) transmission resonances are drastically suppressed for spin electrons tunneling through the symmetric heterostructure under an applied bias; and (2) transmission resonances can be enhanced to optimal resonances for spin-up electrons tunneling through the asymmetric structure with double paramagnetic layers under a certain positive bias, while for spin-down ones tunneling through the same structure, resonances can also be enhanced to optimal resonances under a certain negative bias. Transmission suppression and enhancement originate from magnetic- and electric-field-induced and structure-tuned potentials. Spin-dependent resonant enhancement and negative differential resistances can be clearly seen in the current density. The results shown in this work might shed light on design and applications of spintronic devices.

Hao Wang

Papers

Spin waves in an inhomogeneously magnetized stripe

Particle-hole symmetry breaking and the ν= 5 2 fractional quantum Hall effect

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

Spin-polarized transport through a ZnSe/Zn1−xMnxSe heterostructure under an applied electric field

Spin-resonant suppression and enhancement in ZnSe/Zn 1-x Mn x Se multilayer heterostructures