Band gap calculation,how to choose the Kpoints?

[wkxez]

hello, is there anyone who can help me in the band gap calculation.

my situation is that:
I can calculate the band gap of sigle crystalline graphene, because i know the high symmetrical pionts of the first Brillouin zone of an hexagonal crystalline(M-G-K-M).
But the problem is that:
if i want to add some defects in graphene, I need to construct the unit cell in rectangular lattice style. Therefore, I can't use the high symmetrical pionts as before. So I want to know how to choose the Kpoints in this condition.
Should I use the the high symmetrical pionts of the first Brillouin zone of the rectangular lattice? Or I can simply scan these Kpions in the kx or ky direction?
I find some paper that calculates band structure in one direction(G-X), but i don't know what's the meaning of getting the band structure in one direction. If the band gap calculated in this direction can represent the band gap of the materials?
Thanks for your attention.

 

[daveyrocket]

The band gap shouldn't be calculated just from high symmetry points. It should be calculated by taking a mesh of k-points within the zone, the denser the better.

 

[wkxez]

Thanks for your reply. i know what you say. What I really want to know is how to choose the path for the mesh.

 

[M Quack]

Find what parts of the BZ are related through symmetry. E.g. you only need 1/6 because you have 6-fold rotational symmetry. Taking mirror planes into account you can reduce this further.

Keep only the smallest "pie slice" possible. Sometimes you can cut bits and re-attach them elsewhere (in a symmetry-equivalent position) to get a more regular shape that is more easily covered by a regular grid.

If you have done this properly, then all high symmetry axes should be in or on the edge of your slice.

Run a test calculation on a few random points to figure out how long each point takes.
Determine the number of points you can calculate by dividing the available time by the time needed for 1 point.

Then spread the available points evenly throughout your slice, e.g. in a regular grid, or along high symmetry axes first, and then evenly spaced in between.

 

[wkxez]

Find what parts of the BZ are related through symmetry. E.g. you only need 1/6 because you have 6-fold rotational symmetry. Taking mirror planes into account you can reduce this further.

Keep only the smallest "pie slice" possible. Sometimes you can cut bits and re-attach them elsewhere (in a symmetry-equivalent position) to get a more regular shape that is more easily covered by a regular grid.

If you have done this properly, then all high symmetry axes should be in or on the edge of your slice.

Run a test calculation on a few random points to figure out how long each point takes.
Determine the number of points you can calculate by dividing the available time by the time needed for 1 point.

Then spread the available points evenly throughout your slice, e.g. in a regular grid, or along high symmetry axes first, and then evenly spaced in between.

Thanks. As you said, I can cut the rectangular box into hexgonal box, but it will need more atoms in one unit box in order to make that structure. Maybe it will be costly. Can I use these high symmetry kpoints of rectangular box to get the band gap?