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Hello,

I wrote about this topic many months back, and got some very helpful input from the forum, so I apologize for bringing it up again. However, myself and collaborators are writing a manuscript which relies heavily on the correct interpretation of this, and after revisiting the question I think I may have misinterpreted the answers I got. So I want to make sure I am absolutely clear on how I ought to interpret the planar-averaged electrostatic potential of a heterostructure as obtained from the LOCPOT file with LVTOT=.TRUE.

To repeat the set up, we are exploring electronic interface properties of a heterostructure with the heavy metal Pt and insulating Cr2O3. We expect an internal electric field to develop in this structure due to the differences in work functions/electron affinity between Cr2O3 and Pt. In particular, we want to know the SIGN of the electric dipole, and corresponding electric field, across the Cr2O3-Pt interface.

I attach the output of the LOCPOT file here, corresponding to the Cr2O3-Pt heterostructure in DFT with about 20 angstrom vacuum. The Cr2O3 slab is between ~0.5-0.7 fractional coordinate, and Pt is between ~0.7-1. The remainder is vacuum. I believe based on extensive discussion with admins in this forum that the VASP convention for an electric field is opposite to the normal convention in physics; i.e. in VASP, an electric field points in the direction that a negative test charge, rather than a positive charge, would move. Similarly, electrons will move from a higher to lower electrostatic potential in VASP, rather than the common convention where a positive charge moves from higher to lower electrostatic potential.

Based on this, looking at the plot and thinking of the effective electric field, since the average electrostatic potential in the center of the Pt part is lower than in the Cr2O3 part of the heterostructure, I assumed, and the admins agreed, that the resulting electric field, in the "normal" convention where it points in the direction of movement of a positive test charge, would be from Pt towards Cr2O3 (i.e. from lower to higher potential, as plotted in VASP).

HOWEVER, I now think I may have been backwards in concluding that this was then the sign of the electric dipole/field localized at the interface. Thinking more carefully now, it seems to me that what the LOCPOT is actually indicating is that, based on the potential drop (for electrons) from Cr2O3 to Pt, there will be a MOVEMENT of electrons from the Cr2O3 side of the interface the the Pt side. Thus, in equilibrium, there is a net positive accumulation of charge on the Cr2O3, and negative charge on the Pt, side of the interface that results in a dipole (assuming the chemistry convention where dipoles point from positive to negative) pointing from Cr2O3 to Pt. This means that the interface dipole and corresponding interface electric field is actually in the OPPOSITE direction of the potential difference/electric field indicated by the LOCPOT due to the relative difference in potential energies in the bulklike regions of the two materials.

Basically my confusion I think boils down to how we should interpret a LOCPOT for which the average electrostatic potential is not flat across the heterostructure. If an effective electric field exists across the structure, without opposing potentials all charges would just fly off the materials due to the electric field potential. Obviously this doesn't happen. So when we look at a sloped electrostatic potential as plotted with the LOCPOT, whether that is due to an applied electric field in the DFT calculation or an internal difference in Fermi levels/potential energies across a slab, that's clearly not showing the equilibrium picture; is it then the case that we should interpret these plots as the directions in which charges in the material will become polarized? And then does this mean that we can't use these plots directly to determine the direction of localized dipoles that happen due to polarization via an overall electric field (rather, we have to use physical assumptions as I mentioned above?)

Sorry this question is lengthy; The overarching question I think, minus all the philosophical pondering, is how to determine the direction of the LOCALIZED interface dipole in a heterostructure (and NOT the electric field one would calculate based on just naively taking differences in potential energies of the bulklike regions of a heterostructure).

Thanks a lot in advance!

Sorry to complicate this further, but another point which confuses me is that from our layer-resolved density of states, it is clear that the Fermi level of Cr2O3 is lower than that of Pt (see Fig. 3 of this manuscript, which I was involved in and is the same system we are looking at now https://journals.aps.org/prresearch/abs ... h.6.033263) So it seems to me that this must mean electrons will flow from Pt to Cr at the interface to equilibrate the chemical potentials; but I don't know how to reconcile this with the electrostatic potential of Cr2O3 in the LOCPOT being higher than that of Pt (implying, with VASP's convention based on my revised interpretion, that electrons from from Cr2O3 to Pt); they seem to contradict each other.

One thing I notice is that there is a finite, negative slope in the vacuum region as well; I am quite positive, based on tests of my own https://vasp.at/forum/viewtopic.php?p=29367#p29367 (and e.g. this post from nicolascheng https://ww.vasp.at/forum/viewtopic.php? ... c1132321e2 ) that this corresponds to a positive E field with VASP's convention, and a negative E field with the norm physics convention of a positive test charge. So it does seem to me that the net dipole across the entire slab has to correspond to an effective field pointing from Pt to Cr2O3; but I assume that this then leads to a smaller, localized dipole pointing in the other direction at the interface.

Any thoughts from users of admins would be greatly appreciated.

Dear Sophie,

After speaking with my colleagues, I can answer some of your questions.

1) The electronic charge density is treated as a positive number in VASP, so that will be opposite to the normal textbook convention, where the electronic charge is negative.

2)

Basically my confusion I think boils down to how we should interpret a LOCPOT for which the average electrostatic potential is not flat across the heterostructure.

I believe the strategy is to take the differences in the potential between the two heterostructures put together and then two separate calculations of the local potential separately. You can then calculate the potential difference and evaluate its gradients along different directions

3) I believe you can only determine the total dipole from a ground state calculation. I don't know how you would define a localised dipole. You might try to employ some localised charge analysis (e.g. Bader charges or Wannier charge centres) and use this to make some physical or chemical arguments.

In summary, I am not sure there is a "localised quantity" that you can use to show that there is charge transfer, even if you do some sort of "charge partitioning" between the two materials. One possible route that was suggested was to compute the work function in the presence or absence of CrO\(_3\). If this is positive when compared to just Pt it would indicate that electrons have "left" Pt, while if it's negative it would indicate that electrons have been added to Pt.

Hope this helps. Kind regards,
Pedro