Considered are 80 sets of layer groups, each set consisting of four groups: ordinary single and double, and grey single and double layer groups. The structural properties of layer groups (factorization into cyclic subgroups and the existence of grading according to the sequence of halving subgroups) enable efficient symbolic computation (by the POLSym code) of the relevant properties, real and complex irreducible and allowed (half-)integer (co-)representations in particular. This task includes, as the first step, classification of the irreducible domains based on the group action in the Brillouin zone combined with torus topology. Also, the band (co-)representations induced from the irreducible (co-)representations of Wyckoff-position stabilizers (site-symmetry groups) are decomposed into the irreducible components. These, and other layer group symmetry related theoretical data relevant for physics, layered materials in particular, are tabulated and made available through the web site https://nanolab.group/layer/.
To resolve quantitative mismatch between measurements and the existing theory, we perform systematic theoretical study of the effects of small uniform strain on the electronic properties of single-wall carbon nanotubes. Applied torsion or uniaxial strain induces structural deformations (shifts of the two sublattices, radial and torsional strains induced by the applied uniaxial strain, e.g.), which lead to significantly weaker impact on electronic properties of the strained tube. This damping is more pronounced for torsion. For instance, in tubes with a chiral angle close to 30°, the band gap change is reduced up to 60%. The dominant attenuating factor is the relative shift of the sublattices along the tube axis, manifesting strong electronic coupling with the longitudinal high-energy Raman mode. Obtained results match better the experimental observation of the shifts of optical transition energies and the gauge factor in carbon nanotube based piezoresistive sensors, giving a base for further device development.
We developed a full symmetry implementing method, based on classical molecular dynamics with the Brenner-Tersoff potential, for determining the optimal configuration of homogeneously deformed infinitely long single-wall carbon nanotubes. All nanotubes with diameter less than 1.3 nm are studied. Systematic analysis of the coupling between different types of deformation shows that, in the tubes with chiral angle close to zero and 30°, the torsion-induced circumferential strain is opposite to the induced axial strain. Also, torsion in zigzag tubes induces larger circumferential strain, but in armchair tubes it yields a larger axial strain. The influence of diameter on axial-stretching-induced torsion becomes significant only for narrow tubes. Finally, significant deviation from the linear dependence of axial-strain-induced radial deformation is found for zigzag tubes. The presented results are important for the calculation of electro-optical properties of nanotubes under strain.
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