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.

Ferromagnetic Spots in Graphite Produced by Proton Irradiation

La0.7Ca0.3MnO3 films with thicknesses between 2 and 300 nm were fabricated on LaAlO3, SrTiO3, and (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) substrates using pulsed laser deposition. After annealing at 950 °C in flowing oxygen, on LaAlO3 and LSAT, strain-relaxed epitaxial films of high quality were obtained. The magnetization, resistivity, and magnetoresistance of the films was studied as a function of thickness. Down to a thickness of about 4 nm no decrease of the saturation magnetization could be detected; the Curie temperature decreases slightly with thickness in agreement with finite size scaling theory. The thickness dependence of the conductance can be understood as a size-effect in thin films; there is no indication of an electrically dead interfacial layer.

Thickness dependent magnetic and magnetotransport properties of strain-relaxed La0.7Ca0.3MnO3 films

Magnetism in photopolymerized fullerenes

The microstructural, magnetic, and magnetotransport properties of ${\mathrm{La}}_{0.7}{\mathrm{Ca}}_{0.3}{\mathrm{MnO}}_{3}$ films epitaxially grown on ${\mathrm{SrTiO}}_{3}$ substrates were studied as a function of film thickness. Films with a thickness above 70 nm show bulklike properties consistent with the relaxed film growth. Very thin films are fully strained and are insulating and ferromagnetic in zero field. Under the application of a large magnetic field a strongly hysteretic metal-insulator transition is seen accompanied by a transition to a ferromagnetic state with larger saturation magnetization. The field-induced metallic state is shown to be anisotropic with metallic domains extending along the field direction. An analysis of the microstructure shows that the strain variation across growth islands is far too small to induce strain-related phase separation on length scales of the order of 100 nm. It is concluded that the insulating state is a property of homogeneously strained manganite films and arises from a weakening of the double-exchange interaction due to the ordering of atomic orbitals.

K.-H. Han

Papers

Induced magnetic ordering by proton irradiation in graphite.

Ferromagnetic Spots in Graphite Produced by Proton Irradiation

Thickness dependent magnetic and magnetotransport properties of strain-relaxed La0.7Ca0.3MnO3 films

Magnetism in photopolymerized fullerenes

Strain-induced orbital ordering in thin La 0.7 Ca 0.3 MnO 3 films on SrTiO 3