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We consider a relaxation of the concept of well-covered graphs, which are graphs with all maximal independent sets of the same size. The extent to which a graph fails to be well-covered can be measured by its independence gap, defined as…
There exist three conformers of hydrogenated graphene, referred to as chair-, boat-, or washboard-graphane. These systems have a perfect two-dimensional periodicity mapped onto the graphene scaffold, but they are characterized by a $sp^3$…
We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a…
The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this paper we found non-dispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as…
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different…
In this Letter, we put forward a resolution to the prolonged ambiguity in energy band gaps between theory and experiments of fabricated graphene nanoribbons (GNRs). Band structure calculations using density functional theory are performed…
Inspired by the unique properties of graphene, the focus in the literature is now on investigations of various two-dimensional (2D) materials with the aim to explore their properties for future applications. The group IV analogues of…
Symmetry arguments are used to describe all possible two-dimensional periodic corrugations of graphene ("nanomeshes") capable of inducing tangible semiconducting gap. Such nanomeshes or superlattices break the initial graphene translational…
While numerous methods have been proposed to produce semiconducting graphene, a significant bandgap has never been demonstrated. The reason is that, regardless of the theoretical gap formation mechanism, disorder at the sub-nanometer scale…
The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of…
Recent experimental findings and theoretical predictions suggest that nitrogen-doped CVD-grown graphene may give rise to electronic band gaps due to impurity distributions which favour segregation on a single sublattice. Here we demonstrate…
The design and development of new photonic devices for technological applications requires a deep understanding of the effect of structural properties on the resulting band gap size and its position. Here, we perform a theoretical study of…
Using a tight-binding model, we study a line defect in graphene where a bulk energy gap is opened by sublattice symmetry breaking. It is found that sublattice symmetry breaking may induce many configurations that correspond to different…
A blueprint for producing scalable digital graphene electronics has remained elusive. Current methods to produce semiconducting-metallic graphene networks all suffer from either stringent lithographic demands that prevent reproducibility,…
In this research has been studied the possibility of existence the neutral triplet collective mode in undoped graphene and graphite without one-cone approximation. This work tries to study this collective mode from different points of view.…
We have used scanning tunneling microscopy and spectroscopy to resolve the spatial variation of the density of states of twisted graphene layers on top of a highly oriented pyrolytic graphite substrate. Owing to the twist a moire pattern…
Helical twisted trilayer graphene exhibits zero-energy flat bands with large degeneracy in the chiral limit. The flat bands emerge at a discrete set of magic twist angles and feature properties intrinsically distinct from those realized in…
The tight-binding model of bilayer graphene is used to find the gap between the conduction and valence bands, as a function of both the gate voltage and as the doping by donors or acceptors. The total Hartree energy is minimized and the…
A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic assembly of discs, the two species…