[Pw_forum] method to create high-symmetry k-paths?

[Giovanni Pizzi]

Hi,
thanks for your message.

I’d like to add a more detailed explanation for those who are interested in the details.
Indeed, our work https://arxiv.org/abs/1602.06402 cites and takes inspiration on the paper you mention by Setyawan and Curtarolo (SC). The SC paper was the first to introduce the concept of standardisation of crystal structures and band paths for high-throughput, and to derive explicitly the coordinates of irrational k-points and BZ edges.

Our work was meant to improve some issues of that paper.
A detailed discussion on the improvements can be found in our paper, but the most important points are, in my view:

- for some space groups, it is not sufficient to just inspect the Bravais lattice. Instead, the path must depend on the spacegroup. The simplest case is the simple cubic lattice: if the corresponding symmorphic group does not have 90degree rotation symmetries (or equivalently mirror symmetries w.r.t. the {110} planes), additional lines must be considered, along which the bands will differ from the existing paths.
See for example the cP1 example on the SeeK-path website (for spacegroup Pm3), or the band plots at the end of our paper.

-  We always use standard k-point letters as defined in the International Tables and in the Bilbao Crystallographic Server. Moreover, when new letters have to be introduced, then never collide with existing letters from these two standard sources.

- We use standard choices and settings for standardization of the crystal cell, that are based on standard crystallographic conventions (IT tables, and Parthé and Gelato paper [1]). As an an example, in the SC paper, monoclinic lattices are chosen to be unique-axis a, while the standard choice is unique-axis b. Or: for orthorhombic lattices, SC always choose a<b<c; but e.g. for Pmm2 the third axis is fixed by crystallography, and the only condition we can impose is a<b.

There are other details that might differ, as explained in our paper, and in the paper we compare in detail the results obtained with the two methods.

Best,
Giovanni

[1] E. Parthe, L.M. Gelato, Acta Crystallographica Section A, 41 (1985) 142-151.



On 4 Nov 2016, at 07:22, Mohammed Ghadiyali <m786g at live.co.uk<mailto:m786g at live.co.uk>> wrote:

Hi,

This research paper might also help, It contains high symettry path for all systems.

 link: https://arxiv.org/abs/1004.2974

Regards,
Ghdaiyali Mohammed Kader.
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