[Wien] berryphase

[Shahrbano Raheme]

Dear Prof. Rubel and Sheikh,
> Are there total or partial forces? What are the values?

Oops! It was partial force that was large: 
:FOR002:   2.ATOM          6.892          0.000          0.000          6.892 partial forces

Then, I performed one more iteration by adding -fc flag to my run to sum the Hellmann-Feynman, core, and valance forces, run_lapw -fc 1. Here, I would confirm that lambda1 is indeed in its relaxed position since the total forces are very small, as Sheikh also indicated:
:FOR002:   2.ATOM       0.160246       0.000000       0.000000      -0.160246 total forces

So, most of the ambiguities are now made clear by your valuable comments. 

> 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.


Most of our ambiguities originated from lambda0 structure, since it was not cubic. We suspected that the tetragonal lambda1 is created by moving up the atoms of the tetragonal lambda0. This was why when we got nonzero forces, we carelessly thought that the system was under stress. I suggest to change lambda0 structure to a cubic one in the next release of the BerryPi code. In this cases users will more easily realize that a phase transition is occurred from lambda0 to lambda1. This will be also more compatible with the BerryPi paper. For sure, we used the cubic structure, and the result is not changed too much.

​> ​Also you can try to understand more about modern theory of polarization from here http://www.physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf

​Sheikh, I was reading PRB47, 1651 and PRL101, 037210 of David Vanderbilt and his coauthors. Thank you Sheikh, your informed manuscript of David and coworkers will certainly help me. ​
​> ​
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.​​
​
We are thinking about it. Based on the definition of PS, "the change in polarization that occurs when the crystal undergoes  a phase change from the centrosymmetric structure to a structure without an inversion symmetry (Ps=Pnc-Pc)" as given in the BerryPi paper, we are not sure whether we can use the following trick to create the noncentrosymmetic structure  from a centrosymmetric structure. 
​The trick is that we apply spin-orbit coupling on the centrosymmetic structure by initso_lapw. In this case initso_lapw will create a new structure with no inversion symmetry.  ​Maybe we can use this structure as our noncentrosymmetric structure.  

What do you think about this trick?

​> ​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.


Do you think that the intermediate is necessary? By transition I meant transition between lambda0 as the centrosymmetric phase and lambda1 as the noncentrosymmetic phase.

Thank you for your cooperation,

Best regards,
SH. Rahimi
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