[Wien] fold2bloch: problem with K - path in hexagonal lattice

[Rubel, Oleg]

Dear Weronika,

thank you for the detailed email. I will try to address your questions.

The utility fold.m takes a desired path and _folds_ it according to folds = [2 2 2]. So, if you set folds = [1 1 1], then your list of point will follow kpath = [1/2 0 0; 0 0 0;  1/3 1/3 0]. When folds /= [1 1 1], it becomes more complicated. The idea is to get a list of _folded_ k-points such that _after_ unfolding they will be on the desired path.

I will get back with more details after looking into your numbers, but there should be no "gaps" in k-space if folded k-points are generated correctly.

Thank you
Oleg

--
Oleg Rubel (PhD, PEng)
Department of Materials Science and Engineering
McMaster University
JHE 359, 1280 Main Street West, Hamilton, Ontario L8S 4L8, Canada
Email: rubelo at mcmaster.ca
Tel: +1-905-525-9140, ext. 24094
Web: http://olegrubel.mcmaster


________________________________________
From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of Wolszczak, Weronika <wolszcw at wfu.edu>
Sent: Thursday, November 19, 2020 19:54
To: wien at zeus.theochem.tuwien.ac.at
Subject: [Wien] fold2bloch: problem with K - path in hexagonal lattice

Dear Wien2k users,

I am trying to unfold a hexagonal 2x2x2 superlattice with fold2bloch tool, but I am having difficulty with getting the right k-path. As my path is rather complicated (GAMMA->M(1/2 0 0)->K(1/3 1/3 1/3)->GAMMA->A(0 0 1/2)->L(1/2 0 1/2)->H(1/3 1/3 1/3)->A(0 0 1/2)), I tried to use the script which was previously advised here (fold.m)

https://github.com/rubel75/fold2Bloch-VASP/blob/master/utils/fold.m

in the following message:
https://www.mailarchive.com/wien@zeus.theochem.tuwien.ac.at/msg18482.html
However, this doesn't work properly (I'm having empty gaps in the unfolded diagram). I tried a much simpler path, like M->GAMMA->K, with the following input:

%% User input

kpath = [1/2 0 0; 0 0 0;  1/3 1/3 0]; % desired k-path after unfolding
npath = [16 16]; % # of points along each segment
folds = [2 2 2]; % multiplicity used to create a supercell

but this also results is a strange list of k-points:

         1         0         0         0         1 1.00
         2        -1         0         0        15 1.00
         3        -2         0         0        15 1.00
         4        -1         0         0         5 1.00
         5        -4         0         0        15 1.00
         6        -1         0         0         3 1.00
         7        -2         0         0         5 1.00
         8        -7         0         0        15 1.00
         9         7         0         0        15 1.00
        10         2         0         0         5 1.00
        11         1         0         0         3 1.00
        12         4         0         0        15 1.00
        13         1         0         0         5 1.00
        14         2         0         0        15 1.00
        15         1         0         0        15 1.00
        16         2         2         0        45 1.00
        17         4         4         0        45 1.00
        18         2         2         0        15 1.00
        19         8         8         0        45 1.00
        20         2         2         0         9 1.00
        21         4         4         0        15 1.00
        22        14        14         0        45 1.00
        23        16        16         0        45 1.00
        24         2         2         0         5 1.00
        25         4         4         0         9 1.00
        26        22        22         0        45 1.00
        27        -7        -7         0        15 1.00
        28       -19       -19         0        45 1.00
        29       -17       -17         0        45 1.00
        30        -1        -1         0         3 1.00

First 15 points seem to be fine, it goes from GAMMA (0,0) to -M ( -7/15, 0, 0) and then from M(7/15, 0, 0) back to GAMMA (1/15, 0, 0). However, the next part it doesn' go to K point (1/3, 1/3, 0), but rather overshoots (22/45, 22/45, 0), and there are only 4 points on the negative side, while points between (-1/3 -1/3 0) and (0 0 0) are missing. It seems to me that something is wrong here. Can someone comment if this is a correct output? I did the same part of the path -K -> GAMMA -> K with XCrysDen and it goes from (-1/3 -1/3 0) to (1/3 1/3 0) without any gaps, and this seems to be reasonable but it doesn't agree well with the output of fold.m.

I'm not familiar with Matlab, but it seems to me that fold.m doesn't work with a hexagonal lattice nor with more complicated paths like (0 0 0 -> 1/2 0 0 -> 1/3 1/3 0 -> 0 0 0). Can someone suggest how I can get the right path? I suppose I can manually split the whole path into segments in XCrysDen and stitch them all together  manually, but then how to treat points which are not going through GAMMA, but which are on the surface of BZ, like M->K? Shall I include a path which goes symmetrically around a* reciprocal lattice vector or rather symmetrically around GAMMA (-K -> M -> K or -K -> -M)? If I will generate a proper k-path manually, is it going to work with fold2bloch and ubs_dots_w2k_octave.m or is it also going to cause some troubles when plotting sections which are at the surface of BZ?


Best regards,
Weronika

--
Weronika Wiktoria Wolszczak
Postdoctoral researcher
TU Delft/Wake Forest University
LinkedIn<https://www.linkedin.com/in/weronika-wolszczak-6a8087a2>/Research Gate<https://www.researchgate.net/profile/Weronika_Wolszczak>/Google Scholar<https://scholar.google.com/citations?user=RKjzu0EAAAAJ&hl=en&oi=ao>