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

[Josue Itsman Clavijo Penagos]

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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