The recently invented cylindrical geometric space defect is applied to the electron behaviour in the system which can be regarded as a simplified model of a double-wall nanotube. By solving the Schrodinger equation in the region of space with cylindrical geometric defect we explore the influence of such geometric defect on the energy gap and charge distribution. The effect is qualitatively similar to the one obtained earlier by means of traditional simulation methods. In general, the geometric approach can not compete with the known methods of theoretical study of the nanostructures, such as molecular dynamics. However it may be useful for better qualitative understanding of the electronic properties of the nanosystems.
Single-wall carbon nanotubes (SWNTs) are best known in their hollow cylindrical shapes, but the ground state of large-diameter tubes actually corresponds to a collapsed dumbbell-like structure, where the opposite sides of the nanotube wall are brought in contact and stabilized by van der Waals attraction. For those tubes, the cylindrical shape is metastable and it is interesting to investigate the energy barrier for jumping from one configuration to another. We calculate the energy barrier for SWNT collapse by considering a transition pathway that consists of an initial local deformation that …
We investigate the effect of curvature on the energy and stability of domain wall configurations in curved cylindrical nanotubes and nanowires. We use micromagnetic simulations to calculate the phase diagram for the transverse wall (TW) and vortex wall (VW) states in tubes, finding the ground state configuration and the metastability region where both types of walls can exist. The introduction of curvature shifts the range for which the TW is the ground state domain wall to higher diameters, and increases the range of metastability. We interpret this behavior to be primarily due to the curvatu…
We present a symmetry-adapted real-space formulation of Kohn-Sham density functional theory for cylindrical geometries and apply it to the study of large X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham equations posed on all of space, we reduce the problem to the fundamental domain by incorporating cyclic and periodic symmetries present in the angular and axial directions of the cylinder, respectively. We develop a high-order finite-difference parallel implementation of this formulation, and verify its accuracy against established planewave and real-space codes. Using …
We investigate how geometry influences spin dynamics in polygonal magnetic nanotubes. We find that lowering the rotational symmetry of nanotubes by decreasing the number of planar facets, splits an increasing number of spin-wave modes, which are doubly degenerate in cylindrical tubes. This symmetry-governed splitting is distinct form the topological one recently observed in cylindrical nanotubes. Doublet modes with half-integer or integer multiple azimuthal periods of the number of facets, split to singlet pairs with lateral standing-wave profiles of opposing mirror-plane symmetries. Furthermo…
The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted e…
We study the geometrical conditions for stabilizing magnetic skyrmions in cylindrical nanostrips and nanotubes of ferromagnetic materials with chiral interactions. We obtain the low-temperature equilibrium state of the system implementing a simulation annealing technique for a classical spin Hamiltonian with competing isotropic exchange and chiral interactions, radial anisotropy and an external field. We address the impact of surface curvature on the formation, the shape and the size of magnetic skyrmions. We demonstrate that the evolution of the skyrmion phase with the curvature is controlled…
In this paper we calculate the elastic scattering cross sections of slow electron by carbon nanotubes. The corresponding electron-nanotube interaction is substituted by a zero-thickness cylindrical potential that neglects the atomic structure of real nanotubes, thus limiting the range of applicability of our approach to sufficiently low incoming electron energies. The strength of the potential is chosen the same that was used in describing scattering of electrons by fullerene C60. We present results for total and partial electron scattering cross sections as well as respective angular distribu…
We report the one-electron spectrum and eigenstates of infinite achiral and chiral $(2m,m)$ carbon nanotubes found by using the analytic solution to the Schrödinger equation for the tight-binding Hückel-type Hamiltonian. With the help of matching the wave functions on the interfaces between the regions, where electrons have different site energies, we find and compare the transmission coefficients for zigzag, armchair and chiral nanotubes subjected to the action of an applied step-like potential. The correspondence between the nanotube band structure and the energy dependence of the transmissi…
A magnetic field, through its vector potential, usually causes measurable changes in the electron wave function only in the direction transverse to the field. Here we demonstrate experimentally and theoretically that in carbon nanotube quantum dots, combining cylindrical topology and bipartite hexagonal lattice, a magnetic field along the nanotube axis impacts also the longitudinal profile of the electronic states. With the high (up to 17T) magnetic fields in our experiment the wave functions can be tuned all the way from "half-wave resonator" shape, with nodes at both ends, to "quarter-wave r…
Quasi-two-dimensional systems may exibit curvature, which adds three-dimensional influence to their internal properties. As shown by da Costa \cite{dacosta}, charged particles moving on a curved surface experience a curvature-dependent potential which greatly influence their dynamics. In this paper, we study the electronic ballistic transport in deformed nanotubes. The one-electron Schrödinger equation with open boundary conditions is solved numerically with a flexible MAPLE code made available as Supplementary Data. We find that the curvature of the deformations have indeed strong effects on …
The quantum dynamics of carriers bound to helical tube surfaces is investigated in a thin-layer quantization scheme. By numerically solving the open-boundary Schr$\ddot{\rm o}$dinger equation in curvilinear coordinates, geometric effect on the coherent transmission spectra is analysed in the case of single propagating mode as well as multimode. It is shown that, the coiling endows the helical nanotube with different transport properties from a bent cylindrical surface. Fano resonance appears as a purely geometric effect in the conductance, the corresponding energy of quasibound state is obviou…
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. When a suspended nanotube is made into a transistor, frequency shifts of its mechanical resonances allow precise measurement of the adsorbed mass down to the single-atom level. Here we show that its electrical characteristics are also modified by the adsorbed atoms and molecules, partly as a result of a small charge transfer between them and the carbon surface.…
Carbon Nanotubes (CNs) are made of tubular graphite layers. These macromolecules have interesting features which are generally introduced in the first chapter of the thesis. In the rest of the thesis, the light conduction in metallic CNs is investigated. In chapter 2, by modeling metallic single-wall CNs as 2D free electron gas layers, we find the density of electrons on a 2D electron gas and solve the Maxwell's equations for these cylindrical waveguides. We assume the same time-dependency or frequency for the electrons oscillations on the 2D gas layers and the propagating electromagnetic wave…
The magnetization reversal of three-segment cylindrical nanoelements comprising of alternating nanowire and nanotube sections is investigated by means of Monte Carlo simulations. Such nanoelements may feature a three-state behaviour with an intermediate plateau in the hysteresis curve due to a metastable pinning of the domain walls at the wire-tube interfaces. It turns out that vortex as well as transverse domain walls contribute to the magnetization reversal. By varying the geometric parameters, the sequence, or the material of the elements the nucleation location of domain walls, as well as …
We show that quantum confinement in the valence and conduction bands of semiconducting single-walled carbon nanotubes can be engineered by means of artificial defects. This ability holds potential for designing future nanotube-based quantum devices such as electrically driven room-temperature single-photon sources emitting at telecom-wavelength. Using Ar$^{+}$ and N$^{+}$ ion-induced defects, intrananotube quantum dots with sub-10 nm lateral sizes are created, giving rise to quantized electronic bound states with level spacings of the order of 100 meV and larger. Using low-temperature scanning…
Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative description of the conduction electrons' behavior. The confinement process of a quantum particle to a curve or surface leads us, in the so-called "confining potential formalism" (CPF), to a geometry-induced potential (GIP) in the effective Schrödinger equation. With these considerations, this work aims to study in detail the consequences of constraining a quan…
Challenges for first-principles methods in theoretical and computational physics: multiple excitations in many-electrons systems and the Aharonov-Bohm effect in carbon nanotubes
