Reciprocal space Hexagon K-points

[markmick]

For the 6 Kappa-points in a reciprocal space hexagon, can anyone clarify the values for those points, relative to Gamma?  I keep seeing different values in literature and vasp, and need this straightened out.  Based on my attached image, I believe the points (omitting the 0-value for z):

(1)  +0.333, +0.333
(2) +0.333, +0.667
(3) +0.333, -0.333
(4) -0.333, -0.333
(5) -0.333, -0.667
(6) -0.333, +0.333

Mark

[Anders Blom]

Not to be dismissive of your question, but it's a really good idea to figure out these kind of problems yourself. That way you actually understand why the coordinates are as they are, instead of just taking someone else's word for it (and as you already can see from your observation of the literature, that can be misleading or confusing).

It's real simple in 2D: you write down the lattice vectors you use, construct the corresponding reciprocal lattice vectors, then draw the 1st Brillouin zone by hand on paper, including the reciprocal vectors. Since you know by definition the K (or kappa) point to be the corners, you can now easily extract the coordinates of these points in units of the reciprocal vectors, which are the numbers you need.

You can then proceed to figure out why they might be different in other papers (for instance, maybe the lattice vectors are chosen in a different way? Hint: there are 2 different definitions for hexagonal lattices, with 120 or 60 degrees between the vectors).

[markmick]

Maybe I should ask the question differently.   When straining a lattice, I've seen two different ways of handling Kappa, as shown below.  Each returns very different results.  But which one is "correct"?   I need to see the change in the length between G-K and G-K', since strain will change k-space dimensions.  My gut reaction is Version 2, but I've seen folks insist on Version 1.  Version 1 is merely a mirror of K, not a different K. 

I need a second (or third) opinion on this for clarification.  I need KPOINTS that shows the difference in distance between G-K and G-K'.   My bandstructures for both of these versions are inconsistent.  Not sure which one I should focus on.

Version 1
0.333333 0.333333 0.000000  ! K
0.000000 0.000000 0.000000  ! G

0.000000 0.000000 0.000000  ! G
-0.333333 0.33333 0.000000  ! K'


Version 2
0.333333 0.333333 0.000000  ! K
0.000000 0.000000 0.000000  ! G

0.000000 0.000000 0.000000  ! G
-0.333333 0.666667 0.000000  ! K'

[Anders Blom]

There is no patent answer to this because the details (i.e. the specific coordinates) depend on which direction you strain in. The same answer as above therefore holds: do the analysis of the actual Brillouin zone of the lattice you work with.

Another thing to note, which is a bit non-trivial to say the least, is that the Dirac point in strained graphene is not necessarily on a high-symmetry point!