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

[Md. Jahid Hasan Sagor]

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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