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Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van-der-Waals and dielectric forces exerted by the tip which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data…
Flat bands play an important role in the study of strongly correlated phenomena, such as ferromagnetism, superconductivity, and fractional quantum Hall effect. Here we report direct experimental evidence for the presence of flat bands,…
In view of the many quantum field theoretical descriptions of graphene in $2+1$ dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the…
Angle-resolved photoemission and X-ray diffraction experiments show that multilayer epitaxial graphene grown on the SiC(000-1) surface is a new form of carbon that is composed of effectively isolated graphene sheets. The unique rotational…
Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative…
Topological line defects in graphene represent an ideal way to produce highly controlled structures with reduced dimensionality that can be used in electronic devices. In this work we propose using extended line defects in graphene to…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…
Graphene, a flat monolayer of carbon atoms tightly packed into a two-dimensional honeycomb lattice (a one atom thick graphite sheet), is presently the hottest material in nanoscience and nanotechnology. Its challenging hypothetical…
Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are…
We study the band dispersion of graphene with randomly distributed structural defects using two complementary methods, exact diagonalization of the tight-binding Hamiltonian and implementing a self-consistent T matrix approximation. We…
Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due…
The formation of graphen-nanotube composites addresses a few basic problems. First, both partners are good donors and acceptors of electrons, which significantly complicates the intermolecular interaction between them leading to a two-well…
Electronic structures of graphene sheet with different defective patterns are investigated, based on the first principles calculations. We find that defective patterns can tune the electronic structures of the graphene significantly.…
A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic…
Theoretical progress in graphene physics has largely relied on the application of a simple nearest-neighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that…
Systems that can be described with the same mathematical models that account for the properties of electrons in graphene are known as graphene-like systems. These include magnons, photons, polaritons, acoustic waves, and electrons in…
Grain boundaries are topological defects that often have a disordered character. Disorder implies that understanding general trends is more important than accurate investigations of individual grain boundaries. Here we present trends in the…
Graphene has been studied in detail due to its mechanical, electrical, and thermal properties. It is well documented that the introduction of dopants or defects in the lattice can be used to tune material properties for a specific…
We study the low-energy electronic transport across periodic extended defects in graphene. In the continuum low-energy limit, such defects act as infinitesimally thin stripes separating two regions where Dirac Hamiltonian governs the…