Related papers: Group theoretical methods to construct the graphen…
Large holes in graphene membranes were recently shown to heal, either at room temperature during a low energy STEM experiment, or by annealing at high temperatures. However, the details of the healing mechanism remain unclear. We carried…
Graphene, a hexagonal sheet of $sp^2$-bonded carbon atoms, has extraordinary properties which hold immense promise for future nanoelectronic applications. Unfortunately, the popular preparation methods of micromechanical cleavage and…
We predict the stability of a new extended two-dimensional hydrocarbon on the basis of first-principles total energy calculations. The compound that we call graphane is a fully saturated hydrocarbon derived from a single graphene sheet with…
Let $G$ be a compact, simply connected simple Lie group. We give a construction of an equivariant gerbe with connection on $G$, with equivariant 3-curvature representing a generator of $H^3_G(G,\Z)$. Technical tools developed in this…
Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are…
Efforts aimed at scaling fabrication processes to the level of single atoms, dubbed atom-by-atom fabrication or atomic fabrication, invariably encounter the obstacle of atomic scale cleanliness. When considering atomic fabrication,…
Compressed hydrogen passes through a series of layered structures in which the layers can be viewed as distorted graphene sheets. The electronic structures of these layered structures can be understood by studying simple model systems- an…
A connected simple graph is said dual-hamiltonian if its vertex set has a $2$-coloring such that each color class induces a tree. We call such a coloring a hamiltonian coloring. We prove that if $G$ is a graph with a certain type of…
The formation of graphene on the (0001) surface of SiC (the Si-face) is studied by atomic force microscopy, low-energy electron microscopy, and scanning tunneling microscopy/spectroscopy. The graphene forms due to preferential sublimation…
Moir\'e superlattices in graphene supported on various substrates have opened a new avenue to engineer graphene's electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated.…
Using first-principles calculations, we show that the formation of carbohydrate directly from carbon and water is energetically favored when graphene membrane is subjected to aqueous environment with difference in chemical potential across…
A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system, based on a combinatorial structure we call a pre-tree, is introduced. In the special case that we refer to as…
Graphite is a well-studied material with known electronic and optical properties. Graphene, on the other hand, which is just one layer of carbon atoms arranged in a hexagonal lattice, has been studied theoretically for quite some time but…
The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation…
We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction…
The nucleation of graphene on a transition metal (TM) surface, either on a terrace or near a step edge, is systematically explored using density functional theory (DFT) calculations and applying the two-dimensional (2D) crystal nucleation…
We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible…
Graphene, made of sp2 hybridized carbon, is characterized with a Dirac band, representative of its underlying 2D hexagonal lattice. Fundamental understanding of graphene has recently spurred a surge of searching for 2D topological quantum…
Graphene and few-layer graphene at high bias expose a wealth of phenomena due to the high temperatures reached. With in-situ transmission electron microscopy (TEM) we observe directly how the current modifies the structure, and vice versa.…
Theoretical study of graphite (graphene) edge is done. The most stable edge orientation is calculated to be a zigzag [110] edge. Possible applications of the result to the formation of different graphitic structures are discussed.