[QE-users] High-symmetry points in Band Structure plot

[Paolo Giannozzi]

It's ok to put large images and data files on an external server (the
mailing list has a limit of 200 kb to message size). Note that bands.x is a
rather primitive tool and the criterion it uses to declare a point as
"high-symmetry point" is "the point were the direction of the path changes".

Paolo

On Thu, Dec 27, 2018 at 10:50 PM MARIA CATERINA CEVALLOS BRENES <
MARIA.CEVALLOS at ucr.ac.cr> wrote:

> El 27-12-2018 14:37, Josue Itsman Clavijo Penagos escribió:
>
> Dear Maria, have a nice research day. Before trying an answer to your
> questions, a kind  reminder of some posting guidelines:
>
> Please always include you affiliation/granting institute.
>
> Present yourself politely, and insofar do not link to other forum/posts
> outside QE-users mailing lists; it's not neither nice nor common practice
> to do that.
>
> Now, regarding your questioning, high-simmetry points in reciprocal space
> are used becaused they best describe the simplest (and the shortest, as far
> as I remember) paths a travelling periodic wave (bloch solutions) can take
> to move out through the crystal; the precise location of those points
> depends on the space group the crystal structure shows.
>
> So if one study the Band structure at those high-simmetry points,
> bassically all the E-k relationship are determined for electrons in the
> material under study.
>
>
> On the computing side,  bands.x produces a x-coordinate values sequence to
> map the k points path in the same order you have specified previously; so,
> if your set the following path for the Si primitive cell (as recommended in *Hinuma
> et al*, *Band structure diagram paths based on crystallography*, *https://arxiv.org/abs/1602.06402
> <https://arxiv.org/abs/1602.06402>*, there are two different recommended
> k-paths for Si, not connected by shortest distances between the U and K
> points)
>
> K_POINTS crystal_b
>
> 0.0000000000 0.0000000000 0.0000000000 10
> 0.5000000000 0.0000000000 0.5000000000 10
> 0.6250000000 0.2500000000 0.6250000000 1
> 0.3750000000 0.3750000000 0.7500000000 10
> 0.0000000000 0.0000000000 0.0000000000 10
> 0.5000000000 0.5000000000 0.5000000000 10
> 0.5000000000 0.2500000000 0.7500000000 10
> 0.5000000000 0.0000000000 0.5000000000 1
>
> bands.x will generate
>
> 10 intermediate k-points in between Gamma->X (Beginning of first path)
> 10 intermediate k-points in between X->U
> 1 k-point at U (End of first path) (When you plot, draw a thick vertical
> line at this point to make clear this is the end of the path and that there
> is no connection with the next point - K - also).
> 10 intermediate k-points in between K-->Gamma (Beginning of second path)
> 10 intermediate k-points in between Gamma->L
> 10 intermediate k-points in between L->W
> 10 intermediate k-points in between W->X
> 1 k-point at X (end of second path)
>
> That is, 62 k-points for the recommended paths Γ—X—U|K—Γ—L—W—X.
>
> By the way, the plot you show in physics.stackexchange.com uses a custom
> selected k-path. One can choose the k-path that best fits/likes oneself,
> but the recommended one is just enough. Citing the hinuma *et al* paper,
> the recommend k-path is the one that "*cover all special wavevector (k
> -vector) points and lines necessarily and sufficiently*".
>
> So you can see/copy/build the suggested k-points path for your different
> structures by uploading your *.cif/*.pw.in files in
> https://www.materialscloud.org/work/tools/seekpath
>
> Hope all of this helps.
>
> Best regards and happy holydays!
>
> *Professor Josué Clavijo, Ph.D.*
> *Christian, born again*
>
> *Assistant Professor*
> Universidad Nacional de Colombia
> Bogotá DC
> Facultad de Ciencias
> Departamento de Química
> 571-3165000 Ext. 14445
>
> josue.clavijo at gmail.com
> jiclavijop at unal.edu.co
>
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>
> Thanks Mr Clavijo. This solved the question I had.
>
> I'm sorry I didn't present myself properly, I honestly wasn't aware of the
> guidelines. And the reason I put the link instead of writing my question
> here was due to format.
>
> By using the institutional mail I cannot put images in certain order, just
> attach them. And also the code chunks look better in that particular web
> forum. But in any case I won't do it again.
>
> Have a nice day and thanks for your help.
>
> Kind regards,
>
> María.
>
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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