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A study of strongly curved graphene magnetization and magnetic susceptibility is carried out. Through a Dirac model complemented with a tight-binding model analysis, we are able to show that mechanical deformations solve the long-standing…

The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with…

Ab initio density functional theory has been used to analyze flexural modes, elastic constants, and atomic corrugations on single and bi-layer graphene. Frequencies of flexural modes are sensitive to compressive stress; its variation under…

The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and out-of-plane conductivities of graphene are expressed…

We demonstrate the existence of localized states in close vicinity of a linear defect in graphene. These states have insulating or conducting character. Insulating states form a flat band, while conducting states present a slowdown of the…

We analyze the effect of tensional strain in the electronic structure of graphene. In the absence of electron-electron interactions, within linear elasticity theory, and a tight-binding approach, we observe that strain can generate a bulk…

The ground-state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and…

Straintronic devices made of carbon-based materials have been pushed up due to the graphene high mechanical flexibility and the possibility of interesting changes in transport properties. Properly designed strained systems have been…

Quantum confinement of graphene carriers is an effective way to engineer its properties. It is commonly realized through physical edges that are associated with the deterioration of mobility and strong suppression of plasmon resonances.…

We study the electronic properties of a novel topological defect structure for graphene interspersed with C558-line defects along the Armchair boundary. This system has the topological property of being topologically three-periodic and the…

We develop a conformal geometric model for grain boundaries in graphene based on a periodic line of alternating disclinations. Within the framework of (2+1)-dimensional gravity, we solve a reduced form of the Einstein equations to determine…

We study the effect of the curved ripples observed in the free standing graphene samples on the electronic structure of the system. We model the ripples as smooth curved bumps and compute the Green's function of the Dirac fermions in the…

The supercell approach enables us to treat the electronic structure of defective crystals, but the calculated energy bands are too complicated to understand or to compare with angle-resolved photoemission spectra because of inevitable zone…

We study alpha, beta, and gamma graphyne, a class of graphene allotropes with carbon triple bonds, using a first-principles density-functional method and tight-binding calculation. We find that graphyne has versatile Dirac cones and it is…

Graphene plasmonics has become a highlighted research area due to the outstanding properties of deep-subwavelength plasmon excitation, long relaxation time, and electro-optical tunability. Although the giant conductivity of a graphene layer…

In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…

Graphene monolayers supported on oxide substrates have been demonstrated with superior charge mobility and thermal transport for potential device applications. Morphological corrugation can strongly influence the transport properties of the…

Graphane is a layered material consisting of a sheet of hydrogenated graphene, with a C:H ratio of 1:1. We study isotopic effects in the properties of chair graphane, where H atoms alternate in a chairlike arrangement on both sides of the…

Variational geometries describing corrugated graphene sheets are proposed. The isothermal thermomechanical properties of these sheets are described by a 2-dimensional Weyl space. The equation that couples the Weyl geometry with isothermal…

The effects of the electron-electron interactions in a graphene layer are investigated. It is shown that short range couplings are irrelevant, and scale towards zero at low energies, due to the vanishing of density of states at the Fermi…