DFPT - Positive phonon frequencies but negative A2F

Running Abinit Response calculations
1

Dear reader,

I’m performing DFPT calculations on a structure for which I get positive phonon energies/frequencies for all atoms, all perturbation directions and across the irreducible BZ. However, during the calculation of the eliashberg function using:

  1. ANADDB routine (following the same routine as in the legacy tutorial on the ABINIT website),
  2. The DFPT routine but using optdriver 7 and eph_task 1,

I get a phonon band structure with negative (imaginary) phonon modes and indeed negative values in my A2F function. but only at qpoint Γ, but this gives issues since calculation of the isotropic Tc makes this impossible (or the very least, inaccurate). From my knowledge, if this only occurs at gamma there might be a numerical instability/convergence issues, before I proceed I want to provide some notes on this:

Convergence was done well within 1meV for ngkpt, ecut, tsmear (increasing this might remove it, but then the other bands might get too inaccurate for a physical result, so not sure about this), the rprim and acell parameters were also converged strictly.

  • For the ANADDB routine I calculated the GKK elements using the WF on the full BZ, and what I noticed is that these give a negative (imaginary) phonon mode for a couple of directions at the Γ point (and only at Γ), so the fact that this routine gives imaginary phonon modes is then logical, but I don’t understand why this is the case, since during calculation of the densities all were positive (or zero).

  • For the second routine, only inputs of the merged DEN, POT and WFK files were needed, which all contained positive phonon modes, so the fact that this returned something negative is not entirely logical to me.

things I have tried:

  • using nsphere -1 in anaddb to see which radius returns no more imaginary modes (result: none)
  • Different ASR 0/1/2 (result: only minor difference, nothing major)
  • Increasing ECUT (result: all negative frequencies got more stable, with one even becoming positive, suggesting that it is not the structure itself that is unstable but more numerically I think?)

My next best option is to try and avoid Γ altogether by using shiftk 0 0 0.5 but I need some advice on this since I don’t know if the resulting DEN and GKK/POT files will be able to be interpolated correctly at gamma (or if it will work at all)?

Does anyone have some suggestions perhaps?

I included the phonon wavevector results of the DFPT calculation in the file together with (some) of the input to show what I mean, if needed I can include more.

Regards, William

NbSe2H2_xi_xi_migdal.abi (2.8 KB)

Supporting information.txt (4.1 KB)

NbSe2H2_xi_xi_anaddb.in (18.4 KB)

2

Dear William,

If I understand correctly your problem, you are dealing with a system that has a CDW instability in its high symmetry phase. The phonon wavevector in which the instability is present is around q = (1/3, 0, 0) (well to be more precise there is a whole range of negative phonon wavevectors in the harmonic treatment of phonons but the minimum is around the q I mentioned).

If you need a resolve outside of the CDW instability, a possible solution is to increase the electronic temperature (or smearing) until the imaginary phonon modes disappear. For this there are plenty of studies to give you an indication, but if I remember correctly an electronic temperature above 50 meV renders the system dynamically stable.

It is strange though that you see imaginary phonon modes at Gamma. From your files I see that you are treating a system with 8 atoms but the bulk 2H phase of NbSe2 has 2 formula units per unit cell, meaning 6 atoms. Is it possible that you are treating in the DFPT a supercell? This might fold some of the imaginary q vectors back to Gamma, thus the presence of imaginary phonon modes at Gamma.

Let me know!

Bogdan

3

Dear Bguster,

Thank you for the comment, indeed 2H-NbSe2 has a CDW present at (1/3 0 0) but i am treating NbSe2+2H with extra hydrogen atoms, this is why there are 8 atoms. These cause the CDW at 1/3 0 0 to become real. This is why it’s strange to me that gamma is now imaginary all of a sudden, especially since they are acoustic at q=0.

For the smearing, I was considering doing this but I’m not too knowledgeable on this topic, I converged the smearing parameter such that the phonon band structure does not change in the order of 1 meV (so around the phonon energy order) when decreasing the smearing parameter. I was indeed aware of the studies with high smearing, but the goal is ultimately to get a physical result with converged smearing.
update: I did test it but I’d have to increase smearing by 2 orders to get positive results, which ultimately changed the other bands too much.

regards, william