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

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The reported thermal conductivity (κ) of suspended graphene, 3000 to 5000 watts per meter per kelvin, exceeds that of diamond and graphite. Thus, graphene can be useful in solving heat dissipation problems such as those in nanoelectronics. However, contact with a substrate could affect the thermal transport properties of graphene. Here, we show experimentally that κ of monolayer graphene exfoliated on a silicon dioxide support is still as high as about 600 watts per meter per kelvin near room temperature, exceeding those of metals such as copper. It is lower than that of suspended graphene because of phonons leaking across the graphene-support interface and strong interface-scattering of flexural modes, which make a large contribution to κ in suspended graphene according to a theoretical calculation.

http://science.sciencemag.org/content/sci/328/5975/213.full.pdf

Two-Dimensional Phonon Transport in Supported Graphene

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

Using scanning tunneling microscopy in an ultrahigh vacuum and atomic force microscopy, we investigate the corrugation of graphene flakes deposited by exfoliation on a Si/SiO 2 (300 nm) surface. While the corrugation on SiO 2 is long range with a correlation length of about 25 nm, some of the graphene monolayers exhibit an additional corrugation with a preferential wavelength of about 15 nm. A detailed analysis shows that the long-range corrugation of the substrate is also visible on graphene, but with a reduced amplitude, leading to the conclusion that the graphene is partly freely suspended between hills of the substrate. Thus, the intrinsic rippling observed previously on artificially suspended graphene can exist as well, if graphene is deposited on SiO 2 .

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Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO 2

We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled by noninteracting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate temperature. Based on this result, we provide simple rules for gate geometries and materials optimized for reducing the negative effect of thermal charge fluctuations on the gate.

Decoherence of Majorana qubits by noisy gates

It is argued that the subtle crossover from decoherence-dominated classical magnetism to fluctuation-dominated quantum magnetism is experimentally accessible in graphene nanoribbons. We show that the width of a nanoribbon determines whether the edge magnetism is on the classical side, on the quantum side, or in between. In the classical regime, decoherence is dominant and leads to static spin polarizations at the ribbon edges, which are well described by mean-field theories. The quantum Zeno effect is identified as the basic mechanism which is responsible for the spin polarization and thereby enables the application of graphene in spintronics. On the quantum side, however, the spin polarization is destroyed by dynamical processes. The great tunability of graphene magnetism thus offers a viable route for the study of the quantum-classical crossover.

Quantum nature of edge magnetism in graphene.

Electronic states at the ends of a narrow armchair nanoribbon give rise to a pair of nonlocally entangled spins. We propose two experiments to probe these magnetic states, based on magnetometry and tunneling spectroscopy, in which correlation effects lead to a striking, nonlinear response to external magnetic fields. On the basis of low-energy theories that we derive here, it is remarkably simple to assess these nonlinear signatures for magnetic edge states. The effective theories are especially suitable in parameter regimes where other methods such as quantum Monte Carlo simulations are exceedingly difficult due to exponentially small energy scales. The armchair ribbon setup discussed here provides a promisingly well-controlled (both experimentally and theoretically) environment for studying the principles behind edge magnetism in graphene-based nanostructures.

Magnetic correlations in short and narrow graphene armchair nanoribbons.

We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states (edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated Fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.

/pdf/effective-models-for-strong-correlations-and-edge-magnetism-5ckif517do.pdf

Manuel J. Schmidt

Papers

Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO 2

Decoherence of Majorana qubits by noisy gates

Quantum nature of edge magnetism in graphene.

Magnetic correlations in short and narrow graphene armchair nanoribbons.

Effective models for strong correlations and edge magnetism in graphene