[QE-users] Regarding polarization unit pC/m versus C/m^2

[jkmodi22]

Dear QE users,

I have two fundamental questions regarding polarization calculated using the 
Berry Phase method.

1. How should one convert the raw polarization printed in the nscf step from 
C/m2 to pC/m?

For example, say for a monolayer system, the printed value of polarization is 
1.0704332  (mod   1.0641566) C/m2, where the polarization quantum is 
Pq=1.0641566 C/m2. First, bring the raw polarization within the interval 
[-Pq/2,+Pq/2].

For this, I subtracted 1.0704332  - 1* 1.0641566 C/m2= 0.0062766 C/m2. Call 
it Pphysical.

Now, to get to pC/m, what should I do? Should I multiply 0.0062766 C/m2 by 
the cell height 20 angstroms (assume the cell height is 20 angstroms) or 
assume a physical thickness of 3-5 angstroms?

For a bilayer system, suppose the actual thickness of the slab is 3 angstrom 
(Zmax-Zmin=3 angstroms). Then physical thickness of the bilayer system will 
be roughly 6 angstroms (twice of 3 angstroms). so here should I multiply the 
polarization value (Pphysical: derived after bringing the raw polarization 
within [-Pq/2,+Pq/2]) by the cell height (assume cell height =20 angstroms) 
or should I multiply by the physical thickness of the slab (= 6 angstroms)??

2. Secondly, Which is more correct approach to find polarization of a system 
: Planar averaged charged density difference analysis ( which gives only the 
electronic contribution) OR the Berry phase method which gives both the ionic 
and electronic components of the polarization?
This is important for heterobilayer systems.

Kindly help me understand these points.

Thanking you.

Sincerely

Jainandan Modi
Ph.D. Scholar
Electrical Engineering
IIT Kanpur
India
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