Non-zero value of Born effective charge in metallic system

[raihan_ahammed]

Dear Admin and VASP users,

I have been trying to calculate the Born effective charge tensors (Z*) of a bulk metallic system using LEPSILON, with different k-point meshes and smearing settings. Surprisingly, I consistently obtain non-zero (Z*) tensors.

Based on my understanding of this previous discussion (viewtopic.php?t=20517&utm_source=chatgpt.com), I expected (Z*) to vanish for a metallic system, since the non-adiabatic method is not implemented in VASP. Is this interpretation correct, and how should I interpret the non-zero values?

Any clarification or suggestions would be greatly appreciated.

Kind regards,
Raihan

[martin.schlipf]

Your understanding is correct: There should be no Born effective charges in a metallic system. The way this shows up in practice is that the dielectric constant is huge and that your Born effective charges show an erratic convergence behavior. For an insulator you would expect to see a rapid convergence instead. Fundamentally it comes down to a linear response where you have the change of the Fermi occupancies in the numerator and the energy eigenvalues in the denominator. For an insulator the numerator is 1 (occupied - empty) and the denominator is the gap. For a metal both numerator and denominator approach zero and the results become numerically unstable.

As a side note, there are a few potential issues in your INCAR file. Please review that this is what you intended

• you set both ALGO and IALGO
• you set LREAL twice
• you calculate without spin polarization, are you sure Cr does not have a magnetic moment in this compound

[sophie_weber1]

Hello Martin,

I am also involved in this project. Thanks a lot for your quick response.
Your physical explanation makes sense, but then I am a little uncertain how the results in VASP should be interpreted; you seem to be saying that even if your BEC should be zero, you will by default get nonzero values when calculating using LEPSILON, but they will converge erratically. Can you define what you mean (w.r.t which convergence parameters, and what you mean by "erratic") more explicitly? for example, in this system to me the change in BEC with k-mesh did not seem so bizarre or erratic (the number changed appreciable only when the k-mesh was increased dramatically). Or is the printed dielectric constant a better indicator (and what constitutes "huge"?)

If one can't expect to actually get BECs approaching zero in the calculation, even when they should be, it would be useful if some more detailed information regarding how to tell when BEC values are or are not unphysical in the vasp wiki would be very helpful.

More generally, I would expect that if you had a semimetallic, anisotropic system where at least one direction is insulating, once could still get physically meaningful, finite BECs for electric fields along this direction. Can you please clarify whether this is indeed the case, or whether any metallic directions negates the possibilities of BECs?

[martin.schlipf]

I was only partially correct in my last post. While the argument is correct that you need to compute (f_nk - f_mk)/(ε_nk - ε_mk), VASP skips over the critical n = m term instead. Therefore you do not encounter the divergence and the value of Z* actually converges albeit noisy and slowly. Keep in mind that by skipping the n = m term, we do not compute the real Born effective charge and therefore should not expect to reach the value 0. For the dielectric constant the convergence is indeed erratic and small changes to the setup have large changes to the dielectric constant.

As a test, I computed TiN and MgO (both cubic rocksalt structure). You can see that in the metallic system the dielectric constant is erratic, and the Born effective charges converge much slower and do not approach the correct limit.

bec_convergence.png