QuantumATK Forum
QuantumATK => General Questions and Answers => Topic started by: jinylee on March 24, 2014, 07:36
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Dear ATK team,
I tried to calculate polarization which using Berry phase calculation.
Users only can put k-point sampling values in ATK script generator.
As I know, kpoint has typical format as "AxBxC", but in the polarization part of the script generator
there was 3x3 matrix.
At first I put my kpoint values in the diagonal part, but all other part (off-diagonal terms) to be one.
as " 4 1 1
1 12 1
1 1 6 "
After that, I switched the off-terms to be 5, and calculated again.
as " 4 5 5
5 12 5
5 5 6 "
The final polarization values are different with respect to each off-diagonal term of kpoint matrix.
I wonder the meaning of off-diagonal term in kpoint 3x3 matrix.
How I should set the kpoints to calculate polarization?
Thank you in advance.
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First of all, it's easy enough to advise how to choose these 3x3 k-points. Then should be
M N N
N M N
N N M
where M is large and N can be smaller.
The reason it's not just 3 numbers can be seen from the equation defining P_e at http://quantumwise.com/documents/tutorials/latest/Polarization/index.html/chap.introduction.html#sect1.introduction.theory. P_e is a vector with 3 components (XYZ), but for each component you integrate in k-space, with very different kernels for k// and k_| (sorry for poor man's formulas). You need a very accurate integration along k// which for X is along A, and that's your M for "kpoints_a" (4 in your case).
So what you probably need is M=100 and N=3 or 5 or so.