Discrepancy between Fermi levels and electrostatic potential from LOCPOT for heterostructure?

[sophie_weber1]

I thought I would start over with a simpler question since I think I scared everyone away with my last Related to the same topic, I am confused about how to reconcile two difference outputs I have from the same calculation for an insulator-heavy metal heterostructure with vacuum. If I calculate the layer-projected density of states for the heterostructure, I see that in the center of the insulator (Cr2O3) region of the slab, the highest occupied states are below the highest occupied states in the center of the heavy metal (Pt), which sit at the heterostructure Fermi level, marked by the dashed black line. Then I would expect electrons to flow from Pt to Cr2O3 at the interface to try to equilibrate chemical potentials (and indeed, this is what looks to happen for the layers near the interface).

If I plot the electrostatic potential as a function of distance along the slab, with LVTOT=.TRUE. however, I see that the average electrostatic potential (marked by the red line) in the Cr2O3 part of the slab is higher/less negative than the average electrostatic potential in the Pt region of the slab. Since VASP plots the electrostatic potential with respect to electrons, this seems to imply that electrons should flow from Cr2O3 (higher potential) to Pt (lower potential) at the interface. So the exact opposite of what is implied by the density of states. It seems to me like if the highest occupied states in the Cr2O3 region of the slab are lower in energy than in the Pt region as indicated by the DOS, this has to mean that the electrostatic potential of the Cr2O3 region is lower in energy (more tightly bound).

If you can explain how I should understand this apparent discrepancy in the output, I would greatly appreciate it. Also, I'm curious as to what the reference level is set as for the LOCPOT, since it seems that some areas of the Pt potential are actually above zero; perhaps this is because I've included the exchange-correlation energy?

I attached the input files and the image showing the layer-projected density of states and the LOCPOT output which to me seem to contradict each other.

[pedro_melo]

Dear Sophie,

Calculations with heterostructures are not my speciality, so I will try to help as much as I can.

First I need to ask if you followed some of the recommendations written here. It does say that you should avoid plotting the exchange-correlation potential in LOCPOT, and that you should instead set LVHAR=T. From what you wrote you have included the exchange-correlation part. Could you check how the results change without it?

Then, I think that it might be helpful to also look at both the PDOS and the planar averages of the potential of the the isolated structures of Pt and Cr2O3. I do not know where the surface states of Cr2O3 are localised in energy, as you only show results for the interface. This might make it easier to understand how the transfer of electronic density compares to the expected behaviour.

Finally, I think that the values in LOCPOT are not computed with respect to any reference value. This is an issue with all DFT calculations, and that is why when comparing results for isolated Pt and Cr2O3 you should align the vacuum levels, as these are the best reference points.

Let me know if this helps. Kind regards,
Pedro

[sophie_weber1]

Hi Pedro,

Thanks a lot for your detailed response. I am currently running calculation with LVHAR=T rather than LVTOT, so I will see how this changes things.

As for your suggestion of looking at the pdos for the isolated structures, do you mean for the bulk structures, or for the same slab geometries of isolated Cr2O3 and isolated Pt with vacuum? Could you clarify a bit how this analysis could shed light (in particular, how should I compare the planar averages in the two cases)

And finally, if after all this it still seems that the electron transfer at the interface is from Pt to Cr2O3, and the electrostatic potential for electrons still seems to be higher in Cr2O3 than in Pt, do you agree that this seems contradictory? Or am I not thinking about it correctly the two facts can coexist?

Thank you again for your help,
Sophie

[pedro_melo]

Dear Sophie,

I am not an expert on heterostructure calculations, but I will try my best to explain how I would analyse your system.

In my view there are two configurations in your system. The first, the initial state, is where both slabs are far apart and do not interact. If we were to compare their DOS with the vacuum levels aligned, we can try to predict how the charge transfer will occur. The second configuration is the final state, which you computed with VASP. In this case it is as if the charge has already been transferred between the two slabs and the heterostructure is now at a new equilibrium state, i.e. there can be no more transfer of charge between the two slabs. So, from where I see it, one should not look at the final state to predict how charge will be transferred between the two slabs, again because it is as if this transfer has already happened.

This is why I think it is worth to look at the two separate slabs, and by analysing their DOS and/or band structures (with the vacuum levels aligned) it should be possible to predict how charge will be transferred when the heterostructure is created and then compare it to your final result.

Hope this helps clearing up any confusion that I might have caused. Kind regards,
Pedro

[sophie_weber1]

Hi Pedro,

Thanks a lot for the explanation and details, this is helpful and I see your point. I performed the calculations as you said with isolated Cr2O3 and Pt slabs and compared the layer-projected DOS with the vacuum levels aligned (see attached). based on this, since the Fermi level of Pt is below that of Cr2O3 I would expect electrons to be transferred from Cr2O3 to Pt (see attached, where the red is the layer-projected dos for a six-layer slab of isolated Pt, and the blue is for isolated Cr2O3, and the dashed blue lines near zero are the fermi levels after alignment of vacuum, which is the highest dashed black line).

This result seems suprising to me, because this should set up an excess of electrons in Pt and a of holes in Cr2O3, which ought to lead to an internal electric field pointing from Cr2O3 to Pt (in the +z direction in my coordinate system). But based on the negative potential gradient in vacuum (attached, where now it is plotted just with LVHAR=.TRUE. and neglecting the exchange-correlation energy), the electric field for the heterostructure, based on VASP's convention, points in the -z direction (from Pt to Cr2O3, since Cr2O3 is on the bottom, and Pt is on the top, of the heterostructure).

However, I can rationalize this by reasoning that the local charge transfer based on slab differences in Fermi levels might not be the full, or even main, contribution to the internal electric field due to the macroscopic dipole set up in the heterostructure. For instance, I see that atoms at the surface of Cr2O3 interfaced with Pt and those on the surface interfaced with vacuum relax very asymmetrically, so this also sets up a separate charge redistribution that is not captured by the isolated DOS analysis.

But as a final question, to make sure I am interpreting the heterostructure output correctly, could you clarify whether the sign of electric field, as inferred by the slope of the vacuum potential in a heterostructure, will be the same sign of the macroscopic electric field felt "internally" by the heterostructure? I ask for clarification because I know it's generally recommended to turn on dipole corrections in systems with a net dipole, but I don't do this because I want to be able to determine the direction of the resulting internal electric field. So I want to make sure that this calculation is not actually give me artificial, or deceptive, information based on my misunderstanding of how VASP handles slabs with dipoles when one has not set the vacuum correction on.

Thank you for your patience with me, I promise this is the last question about this.