Božidar Nikolić

Symmetry of single-wall nanotubes

Nanotubes have become attractive subjects in solid-state physics owing to their potential applications in nanotechnology. Their symmetry is one of the important tools in theoretical investigations. Here a review is presented of the symmetry groups of the single-wall nano- and microtubes considered in literature: BN, GaN, MS2, C, BC3, BC2N.

Irreducible representations of diperiodic groups

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a generalized translational group and an axial point group. The results are presented in the form of the tables, containing the matrices of the irreducible representations of the generators of the groups. General properties and some physical applications (degeneracy and topology of the energy bands, selection rules, etc) are discussed.

Symmetry based properties of the transition metal dichalcogenide nanotubes

Abstract:The full geometrical symmetry groups (the line groups) of the monolayered, 2Hb and 3R polytypes of the inorganic MoS2 and WS2 micro- and nanotubes of arbitrary chirality are found. This is used to find the coordinates of the representative atoms sufficient to determine completely the geometrical structure of the tubes. Then some physical properties which can be deduced from the symmetry are discussed: electron band degeneracies, selection rules, general forms of the second rank tensors and potentials, phonon spectra.

Symmetry Based Fundamentals of Carbon Nanotubes

Due to pioneering work of Eugen Wigner, Symmetry is well recognized as a clue to understanding physical processes. However, except in Particle Physics, role of Symmetry is mostly conceptual, to give a posteriori profound interpretation of the obtained results. For instance, in Solid State Physics, more than a century known crystal symmetries are applied to describe phase transitions, selection rules, tensor shapes. Probably the only exception is the Bloch theorem, which gives a priori general forms of the electronic quantum states and ionic displacements. However, this theorem treats only the translational symmetry, reducing the calculations to the elementary cell, which is, in many cases, far bellow the maximal possible reduction.

Raman excitation profiles of metallic single-walled carbon nanotubes

In this work Raman excitation profiles of metallic carbon nanotubes have been calculated and thoroughly analyzed. Suppression and vanishing of the high-energy resonance is completely confirmed by our calculations. The presented results clearly show that the suppression, and finally the absence, of the resonance is caused by electron-phonon interaction and interference effects. Electron-phonon coupling for low-energy resonance is significantly larger than for high-energy resonance. Furthermore, the transition energies of those two transitions are close enough to make interference effects important. The type of interference is determined by the sign of the electron-phonon interaction matrix elements. Constructive interference makes the low-energy resonance more intensive and destructive interference destroys the high-energy resonance for most of the metallic tubes.

Optical absorption in molybdenum disulfide nanotubes

Symmetry based calculations of the polarized optical absorption in single-wall MoS2 nanotubes are presented. Optical conductivity tensor for the individual tubes, using line group symmetry implemented POLSym code and DFTB-calculated Slater type orbital functions and Hamiltonian/overlap matrix elements as input data is numerically evaluated. This minimal, full symmetry implementing algorithm enabled calculations of the optical response functions very efficiently and addressing the large diameter tubes and highly chiral tubes (which have huge number of atoms within a unit cell) as well. The absorption spectra dependence on the diameter and chiral angle of the nanotubes is investigated. The results obtained are related to the previously reported measured spectra.

Commensurate Double‐wall Nanotubes: Symmetry and Phonons

For translationally periodic double‐wall carbon nanotubes stable configurations and full symmetry groups are determined. Using this, the phonon dispersions and eigenvectors are calculated and assigned by the complete set of conserved quantum numbers. Breathing‐like modes, friction modes and acoustic modes are studied. The latter are found to be linear in wave vector k.

Optical and Vibrational Spectra of Narrow Nanotubes: A Symmetry Based Approach

By use of the tight binding method for induced representations (based on the line group symmetry) polarized optical conductivity, radial breathing and high energy vibrational mode frequencies of the narrow single‐wall carbon nanotubes are calculated. The absorption spectra features are assigned by the complete set of conserved quantum numbers and the results obtained are discussed in relation to the previously reported calculations and measurements.