Here is a reference telling you how the AFLOW people do it.

dx.doi.org/10.1016/j.commatsci.2010.05.010

What do you mean? Are you asking what the HS points mean or how you can calculate the bands in those points?

I want to ask how to take these HS points and their values. Are these points fixed for different crystal system ? For example if any system has 6 HS points then band structure should be on corresponding 6 HS points or can take at less points.

Here is a reference telling you how the AFLOW people do it.

dx.doi.org/10.1016/j.commatsci.2010.05.010

If I understand correctly, I attach a ppt slide with the most common 3D HS points for fcc lattices and what they mean in terms of vector components (taken from J. Singh's book ISBN-13: 978-0070576070 ISBN-10: 0070576076). Each crystal has its own HS points and when representing bandstructure or phonons the choice of HS points is never unique and often a matter of common practice.

For example, in diamond you can use a reduced representation with only Gamma, X and L, or you can use all the points that I gave you. Since you need to normally show what happens when you move from one HS point to another among all the points you want to show, the more points you choose to show, the more directions and hence zones you need to represent in the plot. 

It really depends what you are trying to show. I recommend you do look at what other people usually do for the crystal structure you want to model.

the link given by Torbjörn Björkman may help you a lot.

Thank You Dear Thomas !

I will go through these links.

Thanks Dear Thomas Mathew !

It will be useful to me, I will go through this reference.

http://www.cryst.ehu.es/

Just another source that i always use. It's a Crystallographic database. They have plenty of things there, to analyse and generate structures. 

Dear Baldissera, I also have same problem. I visited the website you suggested. I am doing following:

I am choosing KVEC "The k-vector types and Brillouin zones of the space groups"  in section "Space Groups Retrieval Tools".  It says:

Please, enter the sequential number of the space group as given in International Tables for Crystallography, Vol. A, or choose it. It gives something like below 

1 P1 2 P-1 3 P2 4 P21 5 C2

6 Pm 7 Pc 8 Cm 9 Cc 10 P2/m

Now, my question is that what should we chose from the table appearing as above. Suppose take an example of well known material graphene. Can you please tell me properly. Thanks

We can start with simple monoclinic space groups. 

Say, Triclinic Space group. It has only two possibilities P1 and P-1. If you add Space group no. 1 and 2 in http://www.cryst.ehu.es/cryst/get_kvec.html. You will found two Brillioun zone, one having many high symmetry points and other with no high symmetry points. 

Now, we will move to software packages like xcrysden and phonopy. Both can predict the space group number for bulk structures quickly. But what about a case like yours "graphene". Assigning of a space group is purely related to symmetry operations.  Phonopy like codes can assign the space group easily to even two-dimensional materials. It might help you in choosing the Brillouin zone. The movement is always from the gamma to nearest high symmetry point, covering the whole path for of Brillouin zone in x-y direction (say for a two-dimensional case).

How to start? We will start simply with the case like graphene.  Make your unit cell. 

Look for lattice parameters like a, b and gamma (angle) for two-dimensional materials.  From this, you can assign the space group to your unit cell. As graphene belongs to hexagonal systems, a=b, and gamma=120. 

Hexagonal 168 to 194, enter the number of space group on the above-mentioned website. You will get the corresponding Brillouin zone. 

186 = G-K-M-G or 168 = G-K-M-G. Both have similar reciprocal space coordinates.

Try to open your structure in xcrysden and look for Wigner-Seitz cell and then for tools>kpath> etc. You can quickly found out high symmetry point for any structure. 

Best suggestions are, please try to look for already reported structures. It might help you in understanding. 

use xcrysden

The best to plot High symmetry line is following Curtarolo paper:

https://arxiv.org/pdf/1004.2974.pdf

or Tanaka which is a bit more simple in the explanation, but more obscure in giving out the details:

https://arxiv.org/pdf/1602.06402.pdf

Then double check what you think is your high symmetry line with Material Prj https://materialsproject.org/

Also look in the literature  with a critic eye since most of the time people provide wrong high symmetry path.

Dear All

@Federico Brivio, @Gustavo Baldissera and @Torbjörn Björkman

Here, I want to ask for bulk system we can take high symmetric KPOINTS path from so many sources like Curtarolo paper and AFLOW website etc. but for surface 110, 100 etc bandstructure calculation how does take high symmetric KPOINTS.

Thank you all for help and support !

Shilendra

I would recommend that you take your relaxed surface and sticks it into a symmetry analyzer again, to get the space group of the structure you actually get. That's the only way really, since the symmetry can change if the surface reconstructs. Then you can just use the relevant k-path for that symmetry.

Dear Dr. Torbjörn Björkman thank you for your answer !

Your mean is that according to relaxed surface symmetry (space group) we have to take high symmetric KPOINTS.

Here I want to ask if I am taking 110 or any surface (without any reconstruction) of any 7 crystal system then after relaxation the surface symmetry (space group) will change from original bulk system.

Is there any online source for checking symmetry of relaxed system.

For my system bulk and 110 surface is showing C_1 symmetry in OUTCAR as

The static configuration has the point symmetry C_1

Thank You

Shilendra

You should scramble all positions prior to the surface relaxation so you don't miss obvious reconstructions. The best way is to use some program that finds symmetries to some given precision and then returns a cif file (or similar) with the space group and everything else in it. I usually go for the FINDSYM program:

http://stokes.byu.edu/iso/findsym.php

The web interface is a little awkward, but if you click around you'll find a compiled unix version for download (I think).

You might also find the (online) SeeK-path tool useful:

http://www.materialscloud.org/tools/seekpath/input_structure/

You can choose standard reference geometries, or upload one of your own. The paper reference is:

Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, I. Tanaka, Band structure diagram paths based on crystallography, Comp. Mat. Sci. 128, 140 (2017). DOI: 10.1016/j.commatsci.2016.10.015

You can do that in Xcrysden. In the section Of K-Path maker you can easily select the points from Brillouin Zone.