[Wien] berryphase

[Oleg Rubel]

Dear Shahrbano,

> ... Although we could reproduce
> the SP of the sample, P_s= P_z(lambda1)- P_z(lambda0) = 0.312113863793-
> 1.52399256575e-11 = 0.312113863777760 C/m^2 which is very close to the
> readme file (but not exactly the same as it P_s= P_z(lambda1)- P_z(lambda0)=
> 0.31140111708550217-1.4486341471349937e-11= 0.3114011170710158 C/m^2), there
> are some things which are not clear for us.

This difference is not material. Tutorials were done with an earlier
version of Wien2k and a default SCF convergence. Possibly, a tighter
convergence will lead to the same result in both cases.

> Why would not define the P_s just as P_z(lambda1)?

In general, P(lambda0) = 0 may not always be true due to pi rapping.
So it will be a very "slippery" assumption. This is why I would insist
on doing both calculations (lambda0, lambda1) even though you might
expect zero.

> We examined these two structures by calculating the exerted forces on the
> atoms of them to check whether they are in their relaxed positions or not.
> We found that the displaced atoms in lambda1.strcut were under
> tension--:FOR002 and :FGL002 are not zero.

Are there total or partial forces? What are the values?

> In the way as discussed in tutorial1, the SP certainly will depend on the
> displacements. If we increase the amount of displacement, then we will
> obtain larger SP.

In any case, you are need a well converged atomic positions. In our
calculations we try to optimize structure to better than 2 mRy/Bohr.
(Sheikh can probably comment more.)

> So, unlike Boron effective charge
> calculations it appears that the SP calculations cannot give a unique
> result?

Indeed, the SP should be unique. There should be only one well
converged structure. Of course, it will be sensitive to the choice of
XC functional.

> 3) And, why we should not fully initialize the centrosymmetric one?

We do not want Wien2k to realize its higher symmetry. Therefore, the
initialization is done for low-symmetry lambda1 case only. Both
structures should have identical symmetry operations in order to
ensure consistency and comparability of the results.

> In summary, according to the definition of SP, a transient from a
> centrosymmetry to a noncentrosymmetry seems to be necessary. But, here both
> of the phases are tetragonal, while in the paper one of them is considered
> to be cubic.

Strictly speaking, you are right. We would need a cubic structure for
lambda0 and you can try it. What you will find in this case that it
does not matter for P(lambda0).

> Where is the transition in this tutorial?

You can make a transition by choosing an intermediate structure (say
lambda05). I am not aware of unique way to define the intermediate
state: we know for sure only lambda0 and lambda1. But you can imagine
lambda1 as a distorted case of lambda0. For lambda05 you need half of
the distortions. Of course, NO optimization of atomic positions should
be performed for lambda05. Otherwise you will end up with lambda1
again.

> What will be the criterion to move up the atoms?

Zero force and stress for lambda1.

> What is the difference between SP and total polarization?

It is the essence of the modern polarization theory that the total
polarization does not make sense. Only a difference matters, i.e. SP.

> Would you discuss how we can find the centrosymmetric and noncentrosymmetric
> ones for any cases?

This part I am not sure, especially for GaN. The thinking should start
with analysis of measurable quantities/effects, which you would like
to model.


Thank you
Oleg