[Pw_forum] About band structure.

Hande Ustunel hande at newton.physics.metu.edu.tr
Fri Aug 8 08:52:43 CEST 2008

Dear Bipul,

> Thanks for helping me. It really works and really solves my problem. Just

Glad it works for you.

> one thing to ask is that, while plotting the bands structure, it generates
> file.xmgr file. The x-axis are the k-points. But my question is the k-points
> are three no. (e.g. like 0.5 0.5 0.5), but it convert it in a single number.

I'm not exactly sure what you are asking but I'll assume that you are
asking how a three-component vector can be represented by a single point on
a plot. Here a good textbook on solid state is what you should be
consulting. What we call the "band structure" is really a complicated
four-dimensional plot : three axes kx, ky, kz and the energy values
corresponding to each of these points. Since it is impossible to draw such
a plot, this scheme has been devised where you pick some high-symmetry
kpoints in the BZ and draw the band structures along lines that are drawn
between these points. You can then represent this on a two-dimensional
plot. Luckily all the interestin things happen between these points. These
points are usually chosen at the edges of the BZ (or sometimes halfway) and
are usually labeled with capital Latin letters (except Gamma) like X, J, M,
J' so on and so forth. So for a cubic lattice, Gamma corresponds to
(0,0,0), X corresponds to (pi/a,0,0) etc. Each of the points you see on the
xmgr plot then corresponds to a point along one of these lines. 

This is a very basic topic so you should be able to read it in any of the
core textbooks such as Kittel or Ashcroft and Mermin. There's a section on
this also in R. Martin's electronic structure book.


Hande Toffoli
Department of Physics
Office 439
Middle East Technical University
Ankara 06531, Turkey
Tel : +90 312 210 3264

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