Related papers: On the linear representations of the symmetry grou…
The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z X {0,1,...,n} X {0,1}, where n is a natural number…
The full symmetry groups for all single- and multi-wall carbon nanotubes are found. As for the single-wall tubes, the symmetries form nonabelian nonsymorphic line groups, enlarging the groups reported in literature. In the multi-wall case,…
The structures and symmetries of single-walled carbon nanotubes (SWNTs) are introduced in detail. The physical properties of SWNTs induced by their symmetries can be described by tensors in mathematical point of view. It is found that there…
For the first time, an approach is suggested for the quantitative description of the electronic structure of single-walled carbon nanotubes and the prediction of active sites for the tube controlled functionalization in view of the tube…
This paper proposes a bottom-up sequence of modeling steps leading to a nanoscopically informed continuum, and as such macroscopic, theory of single-walled carbon nanotubes (SWCNTs). We provide a description of the geometry of the two most…
Carbon nanotubes are modeled as point particle configurations in the framework of Molecular Mechanics, where interactions are described by means of short range attractive-repulsive potentials. The identification of local energy minimizers…
Carbon nanotubes have attracted considerable interest for their unique electronic properties. They are fascinating candidates for fundamental studies of one dimensional materials as well as for future molecular electronics applications. The…
Carbon nanotubes are a feverishly-studied topic in the scientific community as of late. Mathematically, they can be modeled with a quantum graph. Here we consider a structure somewhat similar to carbon nanotubes, another quantum graph that…
This paper is the first one of a series of two articles in which we revisit the optical properties of single-walled carbon nanotubes (SWNT). Produced by rolling up a graphene sheet, SWNT owe their intriguing properties to their cylindrical…
The electronic structure of a graphene sheet is altered when it is rolled up to form a single-walled carbon nanotube (SWCNT), and the curvature effects for small radius nanotubes become significant. In the paper, an analogue of the Bloch…
Newly discovered carbon nanotubes provide an environment in which small atoms move relatively freely. An assembly of such atoms provides a realization of a quasi-one dimensional system which is an ideal testing ground for concepts and…
A top-gated single wall carbon nanotube is used to define three coupled quantum dots in series between two electrodes. The additional electron number on each quantum dot is controlled by top-gate voltages allowing for current measurements…
A single-walled carbon nanotube presents a seamless cylindrical graphene surface and is thus an ideal adsorption substrate for investigating the physics of atoms and molecules in two dimensions and approaching the one-dimensional limit.…
A simple 1D lattice gas model is presented, which very well describes the equilibrium and kinetic behaviors of water confined in a thin carbon nanotube found in an atomistic molecular dynamics(MD) simulation {[} Nature {\bf 414}, 188 (2001)…
Aggregation of carbon nanotubes dispersed in nematic liquid crystalline medium is discussed. A model is proposed, which assumes that the aggregates consist of a "skeleton" formed by stochastically arranged nanotubes and a "shell" ("coat")…
The breaking of symmetry is the ground on which many physical phenomena are explained. This is important in particular for bipartite lattice structure as graphene and carbon nanotubes, where particle-hole and pseudo-spin are relevant…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
The hexagonal lattice and its dual, the triangular lattice, serve as powerful models for comprehending the atomic and ring connectivity, respectively, in \textit{graphene} and \textit{carbon $(p,q)$--nanotubes}. The chemical and physical…
Rolling up of a layer with arbitrary lattice gives nanotube with very reach symmetry, described by a line group which is found for arbitrary diperiodic group of the layer and chiral vector. Helical axis and pure rotations are always…
We report the experimental realization of double quantum dots in single-walled carbon nanotubes. The device consists of a nanotube with source and drain contact, and three additional top-gate electrodes in between. We show that, by…