[Pw_forum] honeycomb lattices and shift in gamma point?

[harman dev]

Dear all,

    This is short extension with reference to my previous message. I
was wondering if this shift in the origin of the Brillouin Zone for
graphene is associated with the honeycomb symmetry. As mentioned, a
hcp cell such as that of Mg has the gamma point as the origin of its
Brillouin Zone whilst the point K seems to be the origin of the
Brillouin Zone for honeycomb lattices such as graphene and boron
nitride. Any comments on this would be great appreciated. Thank you.

Cheers,
Dev


Dear all,

   I am a little perplexed by the definition of some high symmetry
k-points in the hexagonal Brillouin Zone (BZ) of say something like
graphene and Magnesium (Mg). I've carried out a number of nscf type
calculations (to obtain the band structure) for graphene and
magnesium. Typically, one defines the gamma-point as (0,0,0) and the K
point as say something like (0,0.577,0), given a set of b-vectors,
both in units of 2pi/a0. However, I found that whilst this does apply
to bulk Mg, which has a hcp unit cell, the same isn't true for
graphene. In the case of graphene, it appears that in order to
reproduce the bandstructure that we nominally see in literature, the
high-symmetry K point has the coordinates (0,0,0) and the gamma point
as (0,0.577,0)! It "appears" as if the origin has shifted in that
regard and I'm really quite puzzled by this. If I do follow this and
be careful with my selection of k-points in the BZ (using the
b-vectors to define its boundaries and so on and so forth), I do in
fact get the usual band structure of graphene. Whilst this is ok, I'm
not quite contented since I'm not sure as to the actual mechanics of
how the program works. Is there any explanation as to why this is the
case? Note that I am not using a Monkhorst-Pack grid but am actually
specifying the exact k-vectors to be used in the nscf type
calculation. I would really appreciate any feedback on this and any
suggestions.The following is the list of k-points that I used for
graphene, which I should say again, actually generates the correct
band structure:

0.000 0.000 0.000 1.0    !K
0.000 0.192 0.000 1.0
0.000 0.385 0.000 1.0
0.000 0.577 0.000 1.0    !GAMMA
0.083 0.433 0.000 1.0
0.167 0.288 0.000 1.0
0.250 0.144 0.000 1.0    !M
0.167 0.096 0.000 1.0
0.083 0.048 0.000 1.0
0.000 0.000 0.000 1.0    !K

My apologies for the extremely lengthy description of the problem.
Thank you very much for your time and happy computing.

Cheers,
Dev