Carbon Nanotubes Band Assignation, Topology, Bloch States and Selection Rules

Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the single-wall carbon nanotubes are established. The complete set of quantum numbers consists of quasi momenta (angular and linear or helical) and parities with respect to the z-reversal symmetries and, for achiral tubes, the vertical plane. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the same set of quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g. allowed interband transitions, conductivity, Raman tensor, etc.Comment: 11 pages, 2 figures, 2 tables; pdf available from: http://www.ff.bg.ac.yu/qmf/qsg_e.ht

On the linear representations of the symmetry groups of single-wall carbon nanotubes

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 depends on the considered nanotube. We obtain an alternate rather different description by starting from a three-axes description of the honeycomb lattice. In our mathematical model, which is a factor space defined by an equivalence relation in the set {(v_0,v_1,v_2)\in Z^3 | v_0+v_1+v_2\in {0,1}}, the neighbours of an atomic position can be described in a simpler way, and the mathematical objects with geometric or physical significance have a simpler and more symmetric form. We present some results concerning the linear representations of single-wall carbon nanotubes in order to illustrate the proposed approach.Comment: Major change of content. More details will be available at http://fpcm5.fizica.unibuc.ro/~ncotfa

Fermi level quantum numbers and secondary gap of conducting carbon nanotubes

For the single-wall carbon nanotubes conducting in the simplest tight binding model, the complete set of line group symmetry based quantum numbers for the bands crossing at Fermi level are given. Besides linear (k), helical (k'} and angular momenta, emerging from roto-translational symmetries, the parities of U axis and (in the zig-zag and armchair cases only) mirror planes appear in the assignation. The helical and angular momentum quantum numbers of the crossing bands never vanishes, what supports proposed chirality of currents. Except for the armchair tubes, the crossing bands have the same quantum numbers and, according to the non-crossing rule, a secondary gap arises, as it is shown by the accurate tight-binding calculation. In the armchair case the different vertical mirror parity of the crossing bands provides substantial conductivity, though kF is slightly decreased.Comment: 6 pages, 2 figure

HELICALLY COILED CARBON NANOTUBES

Abstract: Helically coiled carbon nanotubes are frequently synthesized, with well elaborated techniques of growth. This paper is a study of stability and conductivity of these configurations within simple theoretical model followed by the numerical approach

The phonon dispersion of graphite by inelastic x-ray scattering

We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the $K$ and $M$ points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the $K$ point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.Comment: 7 pages; submitted to Phys. Rev.

Nanomechanical Properties and Phase Transitions in a Double-Walled (5,5)@(10,10) Carbon Nanotube: ab initio Calculations

The structure and elastic properties of (5,5) and (10,10) nanotubes, as well as barriers for relative rotation of the walls and their relative sliding along the axis in a double-walled (5,5)@(10,10) carbon nanotube, are calculated using the density functional method. The results of these calculations are the basis for estimating the following physical quantities: shear strengths and diffusion coefficients for relative sliding along the axis and rotation of the walls, as well as frequencies of relative rotational and translational oscillations of the walls. The commensurability-incommensurability phase transition is analyzed. The length of the incommensurability defect is estimated on the basis of ab initio calculations. It is proposed that (5,5)@(10,10) double-walled carbon nanotube be used as a plain bearing. The possibility of experimental verification of the results is discussed.Comment: 14 page

Effect of Peierls transition in armchair carbon nanotube on dynamical behaviour of encapsulated fullerene

The changes of dynamical behaviour of a single fullerene molecule inside an armchair carbon nanotube caused by the structural Peierls transition in the nanotube are considered. The structures of the smallest C20 and Fe@C20 fullerenes are computed using the spin-polarized density functional theory. Significant changes of the barriers for motion along the nanotube axis and rotation of these fullerenes inside the (8,8) nanotube are found at the Peierls transition. It is shown that the coefficients of translational and rotational diffusions of these fullerenes inside the nanotube change by several orders of magnitude. The possibility of inverse orientational melting, i.e. with a decrease of temperature, for the systems under consideration is predicted.Comment: 9 pages, 6 figures, 1 tabl

The general fault in our fault lines

Pervading global narratives suggest that political polarization is increasing, yet the accuracy of such group meta-perceptions has been drawn into question. A recent US study suggests that these beliefs are inaccurate and drive polarized beliefs about out-groups. However, it also found that informing people of inaccuracies reduces those negative beliefs. In this work, we explore whether these results generalize to other countries. To achieve this, we replicate two of the original experiments with 10,207 participants across 26 countries. We focus on local group divisions, which we refer to as fault lines. We find broad generalizability for both inaccurate meta-perceptions and reduced negative motive attribution through a simple disclosure intervention. We conclude that inaccurate and negative group meta-perceptions are exhibited in myriad contexts and that informing individuals of their misperceptions can yield positive benefits for intergroup relations. Such generalizability highlights a robust phenomenon with implications for political discourse worldwide

Psycho-social factors associated with mental resilience in the Corona lockdown

The SARS-CoV-2 pandemic is not only a threat to physical health but is also having severe impacts on mental health. Although increases in stress-related symptomatology and other adverse psycho-social outcomes, as well as their most important risk factors have been described, hardly anything is known about potential protective factors. Resilience refers to the maintenance of mental health despite adversity. To gain mechanistic insights about the relationship between described psycho-social resilience factors and resilience specifically in the current crisis, we assessed resilience factors, exposure to Corona crisis-specific and general stressors, as well as internalizing symptoms in a cross-sectional online survey conducted in 24 languages during the most intense phase of the lockdown in Europe (22 March to 19 April) in a convenience sample of N = 15,970 adults. Resilience, as an outcome, was conceptualized as good mental health despite stressor exposure and measured as the inverse residual between actual and predicted symptom total score. Preregistered hypotheses (osf.io/r6btn) were tested with multiple regression models and mediation analyses. Results confirmed our primary hypothesis that positive appraisal style (PAS) is positively associated with resilience (p < 0.0001). The resilience factor PAS also partly mediated the positive association between perceived social support and resilience, and its association with resilience was in turn partly mediated by the ability to easily recover from stress (both p < 0.0001). In comparison with other resilience factors, good stress response recovery and positive appraisal specifically of the consequences of the Corona crisis were the strongest factors. Preregistered exploratory subgroup analyses (osf.io/thka9) showed that all tested resilience factors generalize across major socio-demographic categories. This research identifies modifiable protective factors that can be targeted by public mental health efforts in this and in future pandemics