### Author Topic: How to calculate piezoelectric tensor for a 2D material  (Read 693 times)

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#### Jyotirmoy Deb

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« on: March 1, 2020, 05:09 »
Kindly help me to calculate the piezoelectric tensor for a 2D material. I have calculated for a 2D material using ATK analysis and the coefficient I have obtained are in the units of C/m^2 whereas in most of the papers the coefficient for a 2D material are in the units of C/m.

#### Jyotirmoy Deb

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« Reply #1 on: April 6, 2020, 10:34 »
Dear Sir, I have not received any answer on the given topic. I am eagerly waiting for the response.

#### korand

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« Reply #2 on: December 18, 2020, 16:37 »
there is a same question here

#### Anders Blom

• QuantumWise Staff
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« Reply #3 on: December 18, 2020, 23:25 »
The definition of the polarization does contain a volume normalization factor Omega (https://docs.quantumatk.com/manual/Types/Polarization/Polarization.html) and from what I can tell, we do normalize the results by the total unit cell volume. It seems this will lead to different numbers if you change the size of the vacuum in the direction perpendicular to the 2D sheet, and that would not be physical. It is however possible that this effect is countered by a similar normalization of the wavefunctions.

So you should check explicitly (sorry, I haven't had time to do it myself) if the values of the computed polarization actually depend on the thickness of the vacuum. If it does, then I would consider it more correct to multiply the results by the unit cell height, so that the results are independent of the vacuum length which anyway is arbitrary. But if they don't then actually that would lead to an incorrect value in C/m (one which actually does depend on the vacuum size), and it will be better to keep the number in C/m2.

If so, then possibly (I am not 100% sure though) one could renormalize by the thickness of the 2D material. This is a method commonly used to renormalized a volume density to an area density, but the tricky bit is that the thickness of a 2D material like graphene or even MoS2 is not a well-defined number. In a strict geometric sense, it's zero for graphene, but you could consider it to be the thickness of the electron density, which however is not easy to define uniquely.

Finally, I don't quite agree that all papers will give the number in C/m. See for instance https://www.nature.com/articles/s41699-018-0063-5 which gives all polarizations in C/cm^2. So if you have examples of papers using C/m, I would also ask those authors what thickness they used to normalize with or how they define the polarization, i.e. if they have Omega or some other factor in their formulas (maybe they simply have the area, which would correspond to my first approach above).

#### korand

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« Reply #4 on: April 13, 2021, 11:32 »
I checked it out for MoSe2 and it works. renormalization to the 2D material thickness works.