Gamma point is always the center of Brillouin zone of reciprocal space. If the reciprocal vectors are G_1 and G_2, Gamma point is q=0*G_1+0*G_2. To build the high-symmetry points  you need to find the Brillouin zone first, by

following the Wiegner-Seitz construction, i.e., starting from the first Gamma point (0,0) draw lines to other neighboring Gamma points  built by considering q=n*G_1+m*G_2 with n,m integers. Then, at the middle point between neighboring Gamma points draw a perpendicular line in 2D, or a plane in 3D. Do the same with all neighbors of (0,0). Then you will find a polygon in 2D and a polytope in 3D. For graphene is an hexagon. High symmetry points are the ones at the vertices, like K and K' in graphene. Middle points at the lines are called point M.

In the following link, we show analytically how to do this construction for graphene, even for the case of a distorted honeycomb lattice which is the case of strained graphene,

W. Gómez-Arias, G.G. Naumis, Analytical calculation of electron group velocity surfaces in uniform strained graphene, International Journal of Modern Physics B, Vol. 30, No. 3, 1550263 (2016)

DOI: 10.1142/S021797921550263X

As you will see therein, in 2D is simple to do the construction for any lattice. You do this construction by finding  the equation of the straight lines that passes at the middle points of the Gamma-Gamma line and is perpendicular to it, and then solve the system for finding their intersections with other lines built in the same way, which is a simple problem of two linear equations with two unknowns.

The high symmetry points are given for all the known Bravais lattices. In the following

a paper model of the hexagonal Brillouin zone. Coordinates are in units of the primitive vectors in the reciprocal space.

Best,

A.

http://lampx.tugraz.at/~hadley/ss1/crystaldiffraction/cutoutBZ/hexagonal.pdf

Dear Angelo I found something different in the following link: (have a look at K and H point)

http://lampx.tugraz.at/~hadley/ss1/bzones/hexagonal.php

also one more doubt so any material which crystallizes in hexagonal lattice has same high symmetry points irrespective of 'a' and bond length.

Regards:

Tushar 

Dear Tushar,

I guess your link is reliable (at the end of the website page there is the other link which goes to the pdf file that I attached before!..I don't know the reason why coordinates are different!)

High symmetry points in such sense are critical points related to the primitive unit cell of the reciprocal lattice (Brillouin zone). Their coordinates depend only on the symmetry group which crystalline structure belongs to. The lattice parameter a sure defines your primitive cell and all the coefficients for the unit vectors (both in real and reciprocal space). But symmetry points are irrespective of this latter. Under this perspective it could be thought as a "scale parameter". If you wish, the scale parameter of your unit cell. Supposing that you choose a "supercell" made of 10 primitive cell. Now this is your unit cell in the real space. Having increased 10 times the lattice constant for the new lattice, you have reduced 10 times the dimension of the BZ, but anyway this system belongs to the same symmetry group and fulfill the same symmetry features of the previous one.

Best,

A.

Thanks Angelo

Gamma point is always the center of Brillouin zone of reciprocal space. If the reciprocal vectors are G_1 and G_2, Gamma point is q=0*G_1+0*G_2. To build the high-symmetry points  you need to find the Brillouin zone first, by

following the Wiegner-Seitz construction, i.e., starting from the first Gamma point (0,0) draw lines to other neighboring Gamma points  built by considering q=n*G_1+m*G_2 with n,m integers. Then, at the middle point between neighboring Gamma points draw a perpendicular line in 2D, or a plane in 3D. Do the same with all neighbors of (0,0). Then you will find a polygon in 2D and a polytope in 3D. For graphene is an hexagon. High symmetry points are the ones at the vertices, like K and K' in graphene. Middle points at the lines are called point M.

In the following link, we show analytically how to do this construction for graphene, even for the case of a distorted honeycomb lattice which is the case of strained graphene,

W. Gómez-Arias, G.G. Naumis, Analytical calculation of electron group velocity surfaces in uniform strained graphene, International Journal of Modern Physics B, Vol. 30, No. 3, 1550263 (2016)

DOI: 10.1142/S021797921550263X

As you will see therein, in 2D is simple to do the construction for any lattice. You do this construction by finding  the equation of the straight lines that passes at the middle points of the Gamma-Gamma line and is perpendicular to it, and then solve the system for finding their intersections with other lines built in the same way, which is a simple problem of two linear equations with two unknowns.

Thanks Gerardo

hi Tushar

did you find out the solution?

how to know the X coordinate in 3D?

use xcrysden software ...

Hi,

I found this paper very useful. You can find high symmetry k points for all lattice: Article Setyawan, W. & Curtarolo, S. High-throughput electronic band...