[Pw_forum] Regarding polarisation from Berry phase

[Varadharajan Srinivasan]

Dear all,

I am trying to calculate the polarisation in a system using the Berry phase
approach and I was suffering a confusion regarding the polarisation
quantum.

I want to use a 2-point formula (between polar and non-polar form) to
calculate the polarisation. However, for each structure the polarisation is
calculate modulo a polarisation quantum. I am a little confused as to how
to choose the appropriate polarisation branch. For instance, I got the two
values (in C/m^2) :

0.3848373 (mod  0.3856310) for the polar structure
0.0108830 (mod 0.3856310) for the non polar structure

If I take the numbers as such then the polarisation (difference) is
0.3739543.

However, since the first number is very close to the modulo I could also
chose it to be
-0.0007937 which would then make the polarisation (difference) to
be -0.0116767.

I bring up the latter since I have seen it advised sometimes that the
absolute polarisation should be chosen such that it is much smaller than
the quantum.

In an attempt to resolve the confusion, I also calculated the berry phase
as a function of distortions connecting the non polar to the polar
structure hoping that this would give me some hint. The result is tabulated
below. (D=0 for non-polar and D=1 for polar)

D          Polarisation (C/m^2)
-------------------------------------
0.0          0.0108830
0.25        0.1979569
0.5         -0.1488601
1.0          0.3848373             Mod 0.3856310
------------------------------------

>From this data I would have been convinced with the first method above but
the value for D=0.5 is throwing me off. These numbers are converged with
respect to the k-point mesh as well as the number of points along the
polarisation direction.

Is there an unambiguous way of reading the polarisation from these numbers?
I would really appreciate any helpful hints and advice.

Best,
Vardha.
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