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

To realize graphene-based electronics, various types of graphene are required; thus, modulation of its electrical properties is of great importance. Theoretic studies show that intentional doping is a promising route for this goal, and the doped graphene might promise fascinating properties and widespread applications. However, there is no experimental example and electrical testing of the substitutionally doped graphene up to date. Here, we synthesize the N-doped graphene by a chemical vapor deposition (CVD) method. We find that most of them are few-layer graphene, although single-layer graphene can be occasionally detected. As doping accompanies with the recombination of carbon atoms into graphene in the CVD process, N atoms can be substitutionally doped into the graphene lattice, which is hard to realize by other synthetic methods. Electrical measurements show that the N-doped graphene exhibits an n-type behavior, indicating substitutional doping can effectively modulate the electrical properties of graphene. Our finding provides a new experimental instance of graphene and would promote the research and applications of graphene.

Synthesis of N-Doped Graphene by Chemical Vapor Deposition and Its Electrical Properties

Graphene quantum dots: emergent nanolights for bioimaging, sensors, catalysis and photovoltaic devices

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.

We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particlelike and a holelike band with evanescent wave functions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units has the form $3M+1$, with $M$ an integer, and insulating otherwise. A comparison of the wave functions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.

https://arxiv.org/pdf/cond-mat/0603107.pdf

Electronic states of graphene nanoribbons studied with the Dirac equation

We study the changes in the electronic structure induced by lattice defects in graphene planes. In many cases, lattice distortions give rise to localized states at the Fermi level. Electron-electron interactions lead to the existence of local moments. The RKKY interaction between these moments is always ferromagnetic, due to the semimetallic properties of graphene.

Local defects and ferromagnetism in graphene layers

Single- and few-layer transition metal dichalcogenides have recently emerged as a new family of layered crystals with great interest, not only from the fundamental point of view, but also because of their potential application in ultrathin devices. Here we review the electronic properties of semiconducting $MX_2$, where $M=$Mo or W and $X=$ S or Se. Based on of density functional theory calculations, which include the effect of spin-orbit interaction, we discuss the band structure of single-layer, bilayer and bulk compounds. The band structure of these compounds is highly sensitive to elastic deformations, and we review how strain engineering can be used to manipulate and tune the electronic and optical properties of those materials. We further discuss the effect of disorder and imperfections in the lattice structure and their effect on the optical and transport properties of $MX_2$. The superconducting transition in these compounds, which has been observed experimentally, is analyzed, as well as the different mechanisms proposed so far to explain the pairing. Finally, we include a discussion on the excitonic effects which are present in these systems.

Electronic properties of single-layer and multilayer transition metal dichalcogenides $MX_2$ ($M=$ Mo, W and $X=$ S, Se)

We study the influence of pentagons and heptagons, dislocations, and other topological defects breaking the sublattice symmetry on the magnetic properties of a graphene lattice. It is known that vacancies and other defects involving uncoordinated atoms induce localized magnetic moments in the lattice. Within the Hubbard model the total spin of the nonfrustrated lattice is equal to the number of uncoordinated atoms for any value of the Coulomb repulsion $U$ according to the Lieb theorem. With an unrestricted Hartree-Fock calculation of the Hubbard model we show that the presence of a single pentagonal ring in a large lattice is enough to alter the standard behavior and a critical value of $U$ is needed to get the polarized ground state. Dislocations, Stone-Wales, and similar defects are also studied.

Magnetic moments in the presence of topological defects in graphene

One of the main characteristics of the new family of two-dimensional crystals of semiconducting transition metal dichalcogenides (TMDs) is the strong spin–orbit interaction, which makes them very promising for future applications in spintronics and valleytronics devices. Here we present a detailed study of the effect of spin–orbit coupling (SOC) on the band structure of single-layer and bulk TMDs, including explicitly the role of the chalcogen orbitals and their hybridization with the transition metal atoms. To this aim, we combine density functional theory (DFT) calculations with a Slater–Koster tight-binding (TB) model. Whereas most of the previous TB models have been restricted to the K and K’ points of the Brillouin zone (BZ), here we consider the effect of SOC in the whole BZ, and the results are compared to the band structure obtained by DFT methods. The TB model is used to analyze the effect of SOC in the band structure, considering separately the contributions from the transition metal and the chalcogen atoms. Finally, we present a scenario where, in the case of strong SOC, the spin/orbital/valley entanglement at the minimum of the conduction band at Q can be probed and be of experimental interest in the most common cases of electron-doping reported for this family of compounds.

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Momentum dependence of spin–orbit interaction effects in single-layer and multi-layer transition metal dichalcogenides

One of the main characteristics of the new family of two-dimensional crystals of semiconducting transition metal dichalcogenides (TMD) is the strong spin-orbit interaction, which makes them very promising for future applications in spintronics and valleytronics devices. Here we present a detailed study of the effect of spin-orbit coupling (SOC) on the band structure of single-layer and bulk TMDs, including explicitly the role of the chalcogen orbitals and their hybridization with the transition metal atoms. To this aim, we combine density functional theory (DFT) calculations with a Slater-Koster tight-binding model. Whereas most of the previous tight-binding models have been restricted to the K and K' points of the Brillouin zone (BZ), here we consider the effect of SOC in the whole BZ, and the results are compared to the band structure obtained by DFT methods. The tight-binding model is used to analyze the effect of SOC in the band structure, considering separately the contributions from the transition metal and the chalcogen atoms. Finally, we present a scenario where, in the case of strong SOC, the spin/orbital/valley entanglement at the minimum of the conduction band at Q can be probed and be of experimental interest in the most common cases of electron-doping reported for this family of compounds.

/pdf/momentum-dependence-of-spin-orbit-interaction-effects-in-19pr4g7lwr.pdf

M. P. López-Sancho

Papers

Local defects and ferromagnetism in graphene layers

Electronic properties of single-layer and multilayer transition metal dichalcogenides $MX_2$ ($M=$ Mo, W and $X=$ S, Se)

Magnetic moments in the presence of topological defects in graphene

Momentum dependence of spin–orbit interaction effects in single-layer and multi-layer transition metal dichalcogenides

Momentum dependence of spin-orbit interaction effects in single-layer and multi-layer transition metal dichalcogenides