[QE-users] How to find magnitude of k (wave vector) in hexagonal lattice cell(graphene)?

[Giovanni Cantele]

In the pw.x output you can find:

- a first block of k-points (the one from which you copied the reported
line) that are in 2pi/alat units (as explicitly stated
in the line you copied). That means that they are CARTESIAN COORDINATES (so
k^2 = kx^2 + ky^2 + kz^2),
but scaled by 2pi/a. So you compute |k| and multiply it by this factor
(bewareL if you use a in Angstrom you'll get |k| in Ang^-1,
if you use a in a.u. you' get |k| in a.u.^-1)

- a second block of k-points that are in crystal coordinates, that means
that they are the components along the reciprocal
lattice vectors (listed in the section "reciprocal axes").It's if you take
these ones that you cannot compute |k| by summing the
squares of the individual components

Giovanni
-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it <giovanni.cantele at spin.cnr.it>
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: https://sites.google.com/view/giovanni-cantele/home


Il giorno gio 17 ott 2024 alle ore 21:43 Md. Jahid Hasan Sagor <
md.sagor at maine.edu> ha scritto:

> Hi,
>
> I want to calculate the magnitude of k point(in Brillouin zone) of
> graphene which has a hexagonal unit cell. The lattice parameters of
> graphene are given below:
>
>  &CONTROL
>      calculation = 'scf'
>      /
>      &SYSTEM
>                  ibrav = 4
>                      a = 2.46639
>                      c = 18
>     ATOMIC_SPECIES
>     C 12.0107 C.upf
>     ATOMIC_POSITIONS (crystal)
>     C  0.333333333  0.666666666  0.000000000
>     C  0.666666666  0.333333333  0.000000000
>     K_POINTS (automatic)
>     35 35 1 0 0 0
>
> ibrav 4 has the following lattice vectors.
>
> [image: enter image description here] <https://i.sstatic.net/jckbH7Fd.png>
>
> If I open the scf.out and choose a k point (as follows)
>
> cart. coord. in units 2pi/alat
> k(   44) = (   0.3000000   0.5773503   0.0000000), wk =   0.0300000
>
> How can I calculate the magnitude of the |k| in the hexagonal reciprocal
> unit cell? considering that I know the value of (kx, ky, 0). The lattice is
> a parallelogram so that |k| does NOT simply equal to sqrt(kx^2+ky^2), right?
>
> Best
>
> M J Hasan
> PhD Student
> Mechanical Engineering
> University of Maine
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