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 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

and Applications of Fullerenes, Carbon Dots, Nanotubes, Graphene, Nanodiamonds, and Combined Superstructures Vasilios Georgakilas,† Jason A. Perman,‡ Jiri Tucek,‡ and Radek Zboril*,‡ †Material Science Department, University of Patras, 26504 Rio Patras, Greece ‡Regional Centre of Advanced Technologies and Materials, Department of Physical Chemistry, Faculty of Science, Palacky University in Olomouc, 17 listopadu 1192/12, 771 46 Olomouc, Czech Republic

Broad family of carbon nanoallotropes: classification, chemistry, and applications of fullerenes, carbon dots, nanotubes, graphene, nanodiamonds, and combined superstructures.

Two-dimensional carbon, or graphene, is a semimetal that presents unusual low-energy electronic excitations described in terms of Dirac fermions. We analyze in a self-consistent way the effects of localized (impurities or vacancies) and extended (edges or grain boundaries) defects on the electronic and transport properties of graphene. On the one hand, point defects induce a finite elastic lifetime at low energies with the enhancement of the electronic density of states close to the Fermi level. Localized disorder leads to a universal, disorder independent, electrical conductivity at low temperatures, of the order of the quantum of conductance. The static conductivity increases with temperature and shows oscillations in the presence of a magnetic field. The graphene magnetic susceptibility is temperature dependent (unlike an ordinary metal) and also increases with the amount of defects. Optical transport properties are also calculated in detail. On the other hand, extended defects induce localized states near the Fermi level. In the absence of electron-hole symmetry, these states lead to a transfer of charge between the defects and the bulk, the phenomenon we call self-doping. The role of electron-electron interactions in controlling self-doping is also analyzed. We also discuss the integer and fractional quantum Hall effect in graphene, the role played by the edge states induced by a magnetic field, and their relation to the almost field independent surface states induced at boundaries. The possibility of magnetism in graphene, in the presence of short-range electron-electron interactions and disorder is also analyzed.

https://repositorium.sdum.uminho.pt/bitstream/1822/5177/1/0512091.pdf

Electronic properties of disordered two-dimensional carbon

Proton beam writing

We provide evidence that proton irradiation of energy 2.25 MeV on highly oriented pyrolytic graphite samples triggers ferro- or ferrimagnetism. Measurements performed with a superconducting quantum interferometer device and magnetic force microscopy reveal that the magnetic ordering is stable at room temperature.

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Induced magnetic ordering by proton irradiation in graphite.

The discovery of nanostructured forms of molecular carbon has led to renewed interest in the varied properties of this element. Both graphite and C60 can be electron-doped by alkali metals to become superconducting; transition temperatures of up to 52 K have been attained by field-induced hole-doping of C60 (ref. 2). Recent experiments and theoretical studies have suggested that electronic instabilities in pure graphite may give rise to superconducting and ferromagnetic properties, even at room temperature. Here we report the serendipitous discovery of strong magnetic signals in rhombohedral C60. Our intention was to search for superconductivity in polymerized C60; however, it appears that our high-pressure, high-temperature polymerization process results in a magnetically ordered state. The material exhibits features typical of ferromagnets: saturation magnetization, large hysteresis and attachment to a magnet at room temperature. The temperature dependences of the saturation and remanent magnetization indicate a Curie temperature near 500 K.

Magnetic carbon (Retracted Article. See vol 440, pg 707, 2006)

We have studied the magnetization of various well characterized samples of highly oriented pyrolitic graphite (HOPG), Kish graphite, and natural graphite to investigate the recently reported ferromagneticlike signal and its possible relation to ferromagnetic impurities. The magnetization results obtained for HOPG samples for applied fields parallel to the graphene layers---to minimize the diamagnetic background---show no correlation with the magnetic impurity concentration. Our overall results suggest an intrinsic origin for the ferromagnetism found in graphite. We discuss possible origins of the ferromagnetic signal.

Ferromagnetism in oriented graphite samples

Elemental carbon represents a fundamental building block of matter and the possibility of ferromagnetic order in carbon has attracted widespread attention. However, the origin of magnetic order in such a light element is only poorly understood and has puzzled researchers. We present a spectromicroscopy study at room temperature of proton irradiated metal-free carbon using the elemental and chemical specificity of x-ray magnetic circular dichroism. We demonstrate that the magnetic order in the investigated system originates only from the carbon pi-electron system.

Roland Höhne

Papers

Induced magnetic ordering by proton irradiation in graphite.

Magnetic carbon (Retracted Article. See vol 440, pg 707, 2006)

Ferromagnetism in oriented graphite samples

$π$-Electron Ferromagnetism in Metal Free Carbon Probed by Soft X-Ray Dichroism

Ferromagnetic Spots in Graphite Produced by Proton Irradiation