New era of extensive symmetry applications in physics promote the tools being useful in the group theoretical calculations. In this context Bilbao crystallographic server became one of the cornerstones of the latest breakthroughs, as in many cases brute force calculations were necessary. However, the sub-periodic (line and layer) groups were for a long time completely avoided at such sites. Also, the literature has been reduced to the monograph on the line groups, and encyclopedia. This is even more surprising in the view of the fact that many examples of the crystal band topology are performed for layer groups, while the Su-Heeger-Schriffer model is used to illustrate many of the key-concepts, but without any referring to its full line group symmetry, while some elements of which have been tacitly used. Recently, Bilbao server included some information on the layer groups, which however was far from being complete.
|Site for line and layer groups|
On the other hand, the modified group projector technique developed within NanoLab enables construction of the allowed and irreducible (co)representations of the (single/double ordinary/gray/black-and-white) periodic groups in the most general form, with series of the (co)representations associated to each stratum of the irreducible domain. Also, manipulation with these representations became unrestrictedly automatized. Therefore, it turns out that NanoLab can straightforwardly evaluate and offer to the interested scientific community the sites for line and layer groups with many data, which in some aspects even overwhelm the data given by Bilbao server for space groups. The realization of this stated January 2021, by trial launching of the layer group site.
|Home page for layer groups
||A page with several data for one layer group