[Wien] berryphase

[Shahrbano Raheme]

Dear Prof. Rubel,

 >A quick glance at these references shows that they are discussing zinc 
blende structure as a zero-polarization reference. So you probably need 
to make a zinc blende GaN is the same fashion as wurtzite structure. 
Fig. 12 in [Physics Reports, Volume 428, Issue 1, May 2006, Pages 1-52] 
will be a good starting point, but still not exactly what you need. At 
the end both structures should have identical symmetry and the same # of atoms.

We wish to work on your above comment. But, before going through it, we 
tried to first make sure that we understood the detail of tutorial1 on 
spontaneous polarization (SP) of BaTiO3 sample. 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. So, let us discuss the ambiguities. Maybe clarifying the 
ambiguities in the BiTiO3 sample can help us to find out how to treat 
with our cases.
	1. 1)From the result we see that SP for the centro-symmetric case is almost zero, P_Z(lamda0)=1.52399256575e-11 , as expected.This is expected, because Ti atom is symmetrically surrounded by 6 O atoms, 
as shown in Fig. 4 (a) of Ref. [Com. Phys. Commun. 184 (2013) 647]. 
Therefore, Ti-O polarization vectors cancel each other, which results in negligible SP. The question is that why we need to calculate the 
negligible P_z(lamda0)? Why would not define the P_s just as 
P_z(lambda1)?
	1. 2)We compared lambda0.struct and lambda1.struct by diff command and noticed 
that apart from the positions of the atoms the other things like space 
group, lattice parameters, and son on are similar to each other, see 
below:     
< ATOM  -2: X=0.50000000 Y=0.50000000 Z=0.51517436
---
> ATOM  -2: X=0.50000000 Y=0.50000000 Z=0.50000000
17c17
< ATOM  -3: X=0.50000000 Y=0.50000000 Z=0.97356131
---
> ATOM  -3: X=0.50000000 Y=0.50000000 Z=0.00000000
23c23
< ATOM  -4: X=0.50000000 Y=0.00000000 Z=0.48343742
---
> ATOM  -4: X=0.50000000 Y=0.00000000 Z=0.50000000
25c25
< ATOM  -4: X=0.00000000 Y=0.50000000 Z=0.48343742 
---
> ATOM  -4: X=0.00000000 Y=0.50000000 Z=0.50000000

In Ref. [Com. Phys. Commun. 184 (2013) 647]  two different phases were 
considered, a cubic structure for centrosymmetric phase and a tetragonal structure for the noncentrosymmetric phase. But, in tutorial1 the 
lambda0.struct and lambda1.struct are both tetragonal; none of them are 
cubic, why? 
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. But, there were no forces on 
atoms of lambda0.struct. Ti atom is moved up from Z=0.5 in 
lambda0.struct to Z=0.51517436 in lambda1.struct. If we relax the 
system, maybe lambda1 gets back to lambda0? Both of the phases are 
expected to be in  their relaxed positions, if the phases are really 
existed in nature, and if we would consider the phase transition 
according to the definition of SP.  
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. This situation can be different from the last Born 
effective charge calculations, since in this case we have just moved up 
the atoms, whereas in the Born effective charges two opposite 
displacements have been made which can balance each other. So, unlike 
Boron effective charge calculations it appears that the SP calculations 
cannot give a unique result?

	1. 3)And, why we should not fully initialize the centrosymmetric one? According 
to the tutorial, we should copy lambda1* to lambda0 directory, remove 
lamda1.struct, rename_files lambda1 lambda0, x kgen, x dstart. This 
shows that we are not allowed to initialize the lambda0.struct from 
scratch. Indeed, we did it just to check what happen. When we 
initialized lambda0.struct from scratch by init_lapw -b -vxc 13 -ecut -6 -numk 230 without coping lambda1*, it stopped by error in dstart. We 
traced back the initialization and found that the error was due to the 
symmetry and sgroup program. So, we changed the space group from  (99 P4mm) to (123 P4/mmm) and initialized it, then ran it and did berrypi. The result is:
TOTAL POLARIZATION: 1.41209791237e-11
Which is different from the last one.

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. Where is the transition in this tutorial?
What will be the criterion to move up the atoms?
What will be the role of centrosymmetric if its SP is negligible?
What is the difference between SP and total polarization?
How can one extend SP calculations to an arbitrary case?
Would you discuss how we can find the centrosymmetric and noncentrosymmetric ones for any cases?

Any comments which can help us will be highly appreciated.

Thank for your cooperation.
SH. Rahimi
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