Search results for "Symmetry operation"
showing 8 items of 8 documents
Box 5: Surface Crystallography Terminology
2009
The crystalline nature of the surface differs from the bulk because atoms on the surface experience a different force field due to unterminated bonds, oxidation by adatoms etc. [1]. Free energy minimisation leads to reconstruction of the surface layer from the bulk by formation of dimers and displacement of atoms from their normal sites.
Topological electronic structure and Weyl points in nonsymmorphic hexagonal materials
2020
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and connectivity group theory show that Weyl points are generated by band crossings in accordion-like and hourglass-like dispersion relations. These Weyl points are stable against weak perturbations and are protected by the screw rotation symmetry. Based on first-principles calculations we found a complete agreement between the topological predicted energy dispersion relations and real hexagonal materials. Topological charge (chirality) and Berry curvature calculations…
Symmetries and Symmetry Groups in Quantum Physics
2013
When one talks about discrete or continuous groups which are to describe symmetries of quantum systems, one must first identify the objects on which the elements of these groups are acting.
Symmetry of molecular properties
1993
The symmetry of coefficients in the expansion of a given molecular property are shown to be obtainable through well defined tensor methods. The analytical expansions required of various vibrational and rotational tensors are given up to the fourth degree in dynamical variables. To illustrate the method, some rovibrational properties of spherical tops are considered. The symmetry of the associated molecular constants is expressed, simultaneously, for XY4 and XY6 molecules, by algebraic relations involving the independent constants and the coupling symbols of the molecular symmetry group. To allow comparisons, some examples are given for which the symmetry of the constants has been published …
Electronic structure trends of Möbius graphene nanoribbons from minimal-cell simulations
2014
Investigating topological effects in materials requires often the modeling of material systems as a whole. Such modeling restricts system sizes, and makes it hard to extract systematic trends. Here, we investigate the effect of M\"obius topology in the electronic structures of armchair graphene nanoribbons. Using density-functional tight-binding method and minimum-cell simulations through revised periodic boundary conditions, we extract electronic trends merely by changing cells' symmetry operations and respective quantum number samplings. It turns out that for a minimum cell calculation, once geometric and magnetic contributions are ignored, the effect of the global topology is unexpectedl…
Quantum Simulations of One-Dimensional Nanostructures under Arbitrary Deformations
2016
A powerful technique is introduced for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching. The technique is based on a novel control of periodic symmetry, which eliminates artifacts due to deformation constraints and quantum finite-size effects, and allows transparent electronic structure analysis. Via density-functional tight-binding implementation, the technique demonstrates its utility by predicting novel electromechanical properties in carbon nanotubes and abrupt behavior in the structural yielding of Au7 and MoS nanowires. The technique drives simulations markedly closer to the reali…
The S-kernel: A measure of symmetry of objects
2007
In this paper we introduce a new symmetry feature named ''symmetry kernel'' (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorit…
Visual Discrimination of the 17 Plane Symmetry Groups
2011
Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of…