Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic

Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices

Self-similarity and fractals have fascinated researchers across various disciplines. In graphene placed on boron nitride and subjected to a magnetic field, self-similarity appears in the form of numerous replicas of the original Dirac spectrum, and their quantization gives rise to a fractal pattern of Landau levels, referred to as the Hofstadter butterfly. Here we employ capacitance spectroscopy to probe directly the density of states (DoS) and energy gaps in this spectrum. Without a magnetic field, replica spectra are seen as pronounced DoS minima surrounded by van Hove singularities. The Hofstadter butterfly shows up as recurring Landau fan diagrams in high fields. Electron-electron interactions add another twist to the self-similar behaviour. We observe suppression of quantum Hall ferromagnetism, a reverse Stoner transition at commensurable fluxes and additional ferromagnetism within replica spectra. The strength and variety of the interaction effects indicate a large playground to study many-body physics in fractal Dirac systems.Comment: Nature Phys. (2014

On the eliminating attempts toward Šesták–Berggren equation

Některé nedávné komentáře pochybují o originalitě Šestáka-Berggrenovy rovnice, přestože dosud téměř dosáhla Osm set citačních odpovědí. Hodnota rovnice SB je zkoumána z hlediska obecné logistické rovnice ukazující její Odlišná filozofická strategie od odlišného ortodoxního geometrického modelování v kinetice. Použití připojených výrazů "Zkrácený" a "rozšířený" je zpochybněn.Some recent commentaries doubt the originality of Šesták–Berggren equation even though it received until today almost eight hundred citation responses. The worth of SB equation is examined in terms of general logistic equation showing its divergent philosophical strategy from dissimilar orthodox geometrical modeling in kinetics. The use of appended terms ‘truncated’ and ‘extended’ is questioned

Šesták–Berggren equation: now questioned but formerly celebrated—what is right

Některé současné publikace zpochybňují originalitu Šestákovy-Berggrenovy (Š-B) rovnice, přestože je tato rovnice citována již v 785 případech. SB rovnice je důkladně analyzována a porovnána s jednotlivými geometrickými modely a jinými přístupy. Š-B rovnice je dále studována z hlediska obecné logistické rovnice, díky čemuž je zřejmá odlišná filozofická strategie mezi tradiční geometrickou JMAYK teorií a neslučitelnou kinetikou vyjádřenou dvou parametrickou SB rovnicí. Historie logistického modelování zahrnuje také využití ogivní sigmoidy. Široká aplikovatelnost této rovnice je doložena více než osmdesáti zdroji.Some recent papers doubt the originality of Sˇesta´k–Berggren equation even though it received until today as many as 785 citation responses. The SB equation is thus thoroughly analyzed and weighed against individual geometrical models and rivalry proposals. Moreover, the SB equation is examined in terms of general logistic equation showing divergent philosophical strategy between the traditional geometrical JMAYK versus the incommensurable kinetics through two parametric SB. The history of logistic modeling is revealed including ogive sigmoidal functions. The widespread application is noticed covering as many as eighty references

Valley magnetoelectricity in single-layer MoS2

Magnetoelectric (ME) effect, the phenomenon of inducing magnetization by application of an electric field or vice versa, holds great promise for magnetic sensing and switching applications. Studies of the ME effect have so far focused on the control of the electron spin degree of freedom (DOF) in materials such as multiferroics and conventional semiconductors. Here, we report a new form of the ME effect based on the valley DOF in two-dimensional (2D) Dirac materials. By breaking the three-fold rotational symmetry in single-layer MoS2 via a uniaxial stress, we have demonstrated the pure electrical generation of valley magnetization in this material, and its direct imaging by Kerr rotation microscopy. The observed out-of-plane magnetization is independent of in-plane magnetic field, linearly proportional to the in-plane current density, and optimized when the current is orthogonal to the strain-induced piezoelectric field. These results are fully consistent with a theoretical model of valley magnetoelectricity driven by Berry curvature effects. Furthermore, the effect persists at room temperature, opening possibilities for practical valleytronic devices.Comment: 12 pages, 4 figure