[Pw_forum] Pw_forum Digest, Vol 5, Issue 53

[harman dev]

Thanks for your reply Mike. Yes I do realize that there are many instances
where the reference is taken with respect to the high-symmetry point K. In
those cases, the x-axis is usually taken as (k-K), where small case k is
some k vector taken with respect to the k-vector that is associated with the
point K found at the corner of the hexagonal Brillouin zone. However what I
do not get is why in the pw.x program, the point K is not something like
(1/2,1/sqrt(3))*2pi/a, in Cartesian coordinates. There are of course other
possible combinations, depending on whether you have defined your real space
lattice vectors using a gamma angle of 120 or 60 degrees. But that should
not negate the fact that the true gamma point should have a k-vector of
(0,0). where one would typically observe a large gap between the pi and pi*
bands. Instead, and as mentioned earlier, the pwscf program (pw.x)
calculates the band eigenvalues at each k-point and as it turns out, it is
at and about the k-point (0,0) that the Dirac cone results. This is what I
find strange and puzzling and I'm wondering if the program makes this
artificial "shift" for computational efficiency purposes or for some other
reason that has eluded me. Thanks to all for your time.

Cheers,
Dev


> Dev,
>
> I believe that if you look closely at the published band structures of
> graphene you'll find that many graphs are <em>centered</em> on the K
> point.  This doesn't mean that the K point is now the origin, it just
> means that the K point is the center of the published graph.  That's
> because K is the interesting part of the band structure.
>
> A quick Google (TM) of the web reveals more about graphene than I really
> wanted to know tonight.  Here's a useful tutorial:
>
> http://www.ph.utexas.edu/~macdgrp/meetings/hongki-graphene(partial).pdf<http://www.ph.utexas.edu/%7Emacdgrp/meetings/hongki-graphene%28partial%29.pdf>
>
> Note particularly the band structure on page 8, and compare it to the
> band structure on page 19.
>
>
> harman dev wrote:
> > 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
> >
>
>
> --
>                                        Mike Mehl
>                                        Naval Research Laboratory
>                                        Washington DC USA
>
>
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> End of Pw_forum Digest, Vol 5, Issue 53
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