# How to calculate the band structure?

Hi, all,
I want to calculate the band structure and there is example such like that:

BandLinesScale pi/a
%block BandLines # These are comments

1 0.000 0.000 0.000 \Gamma # Begin at Gamma
50 2.000 0.000 0.000 X # 25 points from Gamma to X
20 2.000 1.000 0.000 W # 10 points from X to W
30 1.000 1.000 1.000 L # 15 points from W to L

40 0.000 0.000 0.000 \Gamma # 20 points from L to Gamma
50 1.500 1.500 0.000 K # 25 points from Gamma to K
20 1.000 1.000 1.000 L # 15 points from W to L
30 2.000 0.500 0.500 W # 10 points from L to U

20 2.000 0.000 0.000 X # 25 points from U to X
Is there anyone can tell me how to define the number of the points and the coordinate of these points? thank you very much

Yours,
Lucy

The coordinates are points at the edge of the first Brillouin zone (except for gamma). If you imagine the 3D Brillouin zone, the points will be either vertices, centers of edges, or centers of faces. You generally have to look those up, as the notation and location of these points depends on your Brillouin zone.

For the number of points, it's a somewhat-arbitrarily assigned number. Usually you would choose the number of points in proportion to the distance between the special coordinates that line segment connects.

The coordinates are points at the edge of the first Brillouin zone (except for gamma). If you imagine the 3D Brillouin zone, the points will be either vertices, centers of edges, or centers of faces. You generally have to look those up, as the notation and location of these points depends on your Brillouin zone.

For the number of points, it's a somewhat-arbitrarily assigned number. Usually you would choose the number of points in proportion to the distance between the special coordinates that line segment connects.

Hi，thank you very much. but I am still confused about the coordinate.
Can you give me an example? Someone said we should choose the symmetry points---special K point. How can we find the highly symmetry point.
Thank you very much
Yours,
Lucy

Well, I already said that high symmetry points are either vertices, centers of edges, or centers of faces of the Brillouin zone. If you want the names (X, K, M, etc.) you have to look them up for your particular Brillouin zone, and for some BZ's they will depend on things like the c/a ratio.

Look at the Brillouin zone for fcc here:
http://en.wikipedia.org/wiki/Brillouin_zone
X is a center of a square face, K and U are centers of an edges, W is a vertex and L is the center of a hexagonal face.

Lucy,

Try to google “table for high symmetry points for brillouin zone” and you should get several web sites that contains table for the coordinates of the high symmetry points for several types of crystals.

Rany