Related papers: Group theoretical methods to construct the graphen…
A simple and effective stepwise-method has been developed to remove defects from the top graphene layers of highly orientated pyrolytic graphite. Using a combination of ozone exposure and moderately high temperature we have shown that a…
Designing new 2D systems with tunable properties is an important subject for science and technology. Starting from graphene, we developed an algorithm to systematically generate 2D carbon crystals belonging to the family of graphdiynes…
Given a compact Riemann surface X with an action of a finite group G, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely…
We investigate the topological phase transitions in graphene under the modulation of circularly polarized light, by analyzing the changes of edge states and its topological structures. A full phase diagram, with up to ten different…
In a recent preprint, Lai and Rohatgi compute the generating functions of lozenge tilings of "quartered hexagons with dents" by applying the method of "graphical condensation". The purpose of this note is to exhibit how (a generalization…
For any finite graph Gamma and any field K of characteristic unequal to 2 we construct an algebraic variety X over K whose K-points parameterise K-Lie algebras generated by extremal elements, corresponding to the vertices of the graph, with…
The electronic properties of a graphene sheet with attached hydrogen atoms is studied using a modified Falicov-Kimball model on the honeycomb lattice. It is shown that in the ground state this system separates into two phases: fully…
We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…
This paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial. Geometric substitution tilings include…
For a group $G$, the generating graph $\Gamma(G)$ is defined as the graph with the vertex set $G$, and any two distinct vertices of $\Gamma(G)$ are adjacent if they generate $G$. In this paper, we study the generating graph of $D_n,$ where…
This study reports the successful synthesis of multilayered graphene sheets via microwave atmospheric pressure plasma. This innovative approach streamlines and expedites graphene production and other carbon nanostructures, eliminating the…
A series of measurements using a technique called electrostatic-manipulation scanning tunneling microscopy (EM-STM) were performed on a highly-oriented pyrolytic graphite surface. The electrostatic interaction between the STM tip and the…
We describe a mechanism that explains the formation of hydrocarbons and hydrocarbyls from hydrogenated graphene/graphite; hard C-C bonds are weakened and broken by the synergistic effect of chemisorbed hydrogen and high temperature…
Two dimensional layers of graphene are currently drawing a great attention in fundamental and applied nanoscience. Graphene consists of interconnected hexagons of carbon atoms as in graphite. This article presents for the first time the…
Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are adjacent if…
When it is oxidized, graphite can be easily exfoliated forming graphene oxide (GO). GO is a critical intermediate for massive production of graphene, and it is also an important material with various application potentials. With many…
Material's geometrical structure is a fundamental part of their properties. The honeycomb geometry of graphene is responsible for the arising of its Dirac cone, while the kagome and Lieb lattice hosts flat bands and pseudospin-1 Dirac…
In this paper we consider tiling $\{p, q \}$ of the Euclidean space and of the hyperbolic space, and its dual graph $\Gamma_{q, p}$ from a combinatorial point of view. A substitution $\sigma_{q, p}$ on an appropriate finite alphabet is…
We propose a new class of materials, which can be viewed as graphene derivatives involving Group IA or Group VIIA elements, forming what we refer to as graphXene. We show that in several cases large band gaps can be found to open up,…
For a fixed integer h>=1, let G be a tripartite graph with N vertices in each vertex class, N divisible by 6h, such that every vertex is adjacent to at least 2N/3+h-1 vertices in each of the other classes. We show that if N is sufficiently…