Related papers: Group theoretical methods to construct the graphen…
Following the discovery of graphene, keen attentions have been paid in comprehending the noticeably superior electromagnetic, optical and absorptive properties of few layer graphene (FLG) with rotational-stacking-faults. With achieving…
A friction based method is proposed for obtaining graphite layers. Freestanding thin structures of graphite containing several layers of graphene are obtained by rubbing a graphite rod on the surfaces of NaCl substrate and then dissolving…
Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates…
Graphene consists of single or few layers of crystalline ordered carbon atoms. Its visibility on oxidized silicon (Si/SiO\_2) enabled its discovery and spawned numerous studies of its unique electronic properties. The combination of…
Consider a curve $\Gamma$ in a domain $D$ in the plane $\boldsymbol R^2$. Thinking of $D$ as a piece of paper, one can make a curved folding $P$ in the Euclidean space $\boldsymbol R^3$. The singular set $C$ of $P$ as a space curve is…
Graphene is locally two-dimensional but not flat. Nanoscale ripples appear in suspended samples and rolling-up often occurs when boundaries are not fixed. We address this variety of graphene geometries by classifying all ground-state…
Substituting each edge of a simple connected graph $G$ by a path of length 1 and $k$ paths of length 5 generates the $k$-hexagonal graph $H^k(G)$. Iterative graph $H^k_n(G)$ is produced when the preceding constructions are repeated $n$…
$\gamma$-Graphyne is the most symmetric sp2/sp1 allotrope of carbon, which can be viewed as graphene uniformly expanded through insertion of two-carbon acetylenic units between all the aromatic rings. To date, synthesis of bulk…
A cheap and flexible method is introduced that enables the epitaxial growth of bilayer graphene on Pt(111) by sequential chemical vapour deposition. Extended regions of two stacked graphene sheets are obtained by, first, the thermal…
The manuscript considers mathematical models for creating a topological drawing of a graph based on the methods of G. Ringel's vertex rotation theory. An algorithm is presented for generating a topological drawing of a flat part of a graph…
While crystalline two-dimensional materials have become an experimental reality during the past few years, an amorphous 2-D material has not been reported before. Here, using electron irradiation we create an sp2-hybridized one-atom-thick…
Strain has been extensively employed to tailor graphene's properties and has emerged as a powerful tool for engineering gauge fields and exploring fundamental phenomena in artificial platforms like photonic graphene. Here we discover that,…
The Ammann A2 tiling is a simple aperiodically ordered tiling of the plane. We consider the graph derived from this tiling, by treating each corner of each tile as a vertex and each side of each tile as an edge. We present a closed-form…
Nearly two-dimensional diamond, or diamane, is coveted as ultrathin $sp^3$-carbon film with unique mechanics and electro-optics. The very thinness ($~h$) makes it possible for the surface chemistry, e.g. adsorbed atoms, to shift the bulk…
The local structure of a tiling is described in terms of a multiplicative structure on its pattern classes. The groupoid associated to the tiling is derived from this structure and its integer group of coinvariants is defined. This group…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
A transfer matrix method is developed for optical calculations of non-interacting graphene layers. Within the framework of this method, optical properties such as reflection, transmission and absorption for single-, double- and multi-layer…
We use our theory of periodized discrete elasticity to characterize defects in graphene as the cores of dislocations or groups of dislocations. Earlier numerical implementations of the theory predicted some of the simpler defect groupings…
Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or…
A novel electrochemical means to generate atomic hydrogen, simplifying the synthesis and controllability of graphane formation on graphene is presented. High quality, vacuum grown epitaxial graphene (EG) was used as starting material for…