sign convention of electric field in VASP?

[sophie_weber]

Hello,

I am trying to figure out the direction of the effective electric field I have in a heterostructure with a potential energy jump across the interface (to be concrete, the electrostatic energy as plotted from the LOCPOT shows a decrease in potential energy as we go from the bottom to the top of the slab moving in the +z direction.

Based on this previous post https://ww.vasp.at/forum/viewtopic.php? ... e24cf62cd9 My understanding is that the test charge convention in VASP for defining an electric field is opposite to the normal convention, i.e. in VASP the test charge is negative. So this means electrons will move along the direction of the electric field.

However, based on this post, my understanding was also that the potential energy difference is still defined as E=-dU/dz. So if I apply an electric field using EFIELD of +.01 eV/ang. the potential energy gradient will still be negative along the +z direction (so it's the potential energy change that an electron would experience in the case of VASP). And this is exactly what the user in the previous post seemed to show, i.e. graphene has a negative potential gradient when he/she applied a positive EFIELD.

However, when I try this as a sanity check, i.e. apply a positive EFIELD=+0.02 eV/angstrom for a symmetric slab with no dipole moment of its own, the potential energy jump along +z is positive, and vice versa for a negative FIELD. This would seem to imply that VASP is defining the potential energy as E=+dU/dz, which contradicts the results of the previous user, and seems like a really odd choice as this would imply that the potential energy and electric field are defined with opposite charge conventions.

So based on this I would take away that the effective electric field in VASP which would produce the decease in potential energy in my heterostructure would be negative, such that the "conventional" direction of the electric field would be positive. Is this right?! And if so, how is that reconciled with the previous user's plots of a positive EfIELD in VASP giving a negative potential gradient? Was the convention changed again since that post?

Thank you very much in advance.

[martin.schlipf]

Perhaps I'm missing something but it looks like your results are consistent with nicholascheng's post. If you look at the vacuum region the slope of the potential is negative for a positive EFIELD.

Does this misunderstanding possibly arise from a confusion of the kink in the potential? If you want to simulate a system with an electric field this leads to a problem with the periodic boundaries. As a consequence somewhere in the unit cell we have to add a kink in the potential to ensure a periodic potential. This kink has no physical meaning which is why we put it as far as possible into the vacuum region. This kink allows to have a slope in the rest of the unit cell proportional to the applied electric field. It is easiest to see this slope if you look at the potential in the vacuum region except for the area where the kink is.

Does this help?

[sophie_weber]

You are absolutely correct; I wasn't seeing the slope at all since it's quite tiny, but when I increase the strength of the field it's quite apparent, and as you say a positive EFIELD gives a negative slope, as expect (see attached).

As you correctly guessed I was getting confused by the direction of the kink and was thinking the "step" in the king went in the same direction as the gradient, but of course it make sense that it would oppose the gradient, i.e. you should have an upward step for a negative gradient.

I'm sorry for my confusion. Then, to confirm that I understand everything with regard to the VASP electrostatic sign conventions, the electrostatic potential as plotted from LOCPOT with LVHAR=.TRUE. gives the potential energy change that an ELECTRON would experience in travelling from one region of the slab to another. So in my "real" case where I have no applied EFIELD but instead a heterostructure with an interface and if I see a negative potential energy change in going across an interface in the +z direction, that means an effective positive EFIELD according to the vasp convention? And thus, with the normal electric field convention where positive charges move along the direction of the electric field, the "normal" electric field should point opposite to EFIELD, in this case in the -z direction of from lower to higher potential energy (as plotted in the LOCPOT; of course if the potential energy were plotted with the positive test charge convention, the change would be opposite).

Is my interpretation correct?

Thank you again so much for your help, and apologies for my confusion!

[martin.schlipf]

Glad to be of help.

I believe your summary is correct in terms of the sign convention used by VASP. I would advise to be careful with the word choices when describing these systems, though. What you observe is a dipole moment or polarization P within your heterostructure. This leads to a electric field E in the vacuum region because the displacement field D is continuous at the surface. This electric field has the same divergent behavior as an external EFIELD. As a side remark, this divergence makes electrostatic corrections crucial for these kind of systems.

[sophie_weber]

Ok, thank you so much! That's a fair point that it's really an electric dipole that occurs in the heterostructure; but in this case the sign considerations are the same I guess, that is, the positive charge of the dipole will be on the side of the interface with higher potential energy, and the negative part of the dipole will be on the side of the interface with lower potential energy, as plotted in LOCPOT; is this the correct way to say it?

Best regards,
Sophie

[martin.schlipf]

Yes, that is correct.

[sophie_weber]

Perfect, thank you, I really appreciate it!

Best wishes
Sophie