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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