ABINIT Discussion Forums

Hi,

I met a problem in calculating born effective charges and dielectric constant of wurtzite GaN using a finite electric field calculation with PAW pseudopotential. The GaN is a polar crystal with spontaneous polarization. In calculation, there are many warnings like following statement:

“berryphase_new : WARNING -
the berry phase has some huge variation in the space of strings of k-points
ABINIT is trying to correct the berry phase, but it is highly experimental”

And the calculated dielectric constant is much larger than experimental value. Does that mean the calculated polarization is not correct? Is this relevant with the spontaneous polarization of wurtzite GaN? And How should we solve this problem?

Thanks,
Daosheng

Hello Daosheng,

1) a few checks first: have you done DFPT calculations of the Born charges? And have you tried norm conserving psp (see pseudo-dojo.org) for the Berry phase version? The former will give you a baseline and is less prone to instabilities, and the latter will tell you if it's a PAW problem

2) the error message appears when abinit tries to rehash the strings of k-points in the Berry phase integrals, to get a smoother behavior of log(det(S)). Basically it complains if the new phase it calculates fluctuates by a quantum of polarization or more. If your final result is not very physical, it's probably failing to clean things, and if the P is bad, the derivatives and epsilon will be too. Perhaps the E field you apply is too strong? Or the cell is shaped strangely such that the quantum is very small? Do you have comparisons to the literature for intermediate quantities like P?

Dear Prof. Verstraete,

Thank you very much for your reply.

Following your suggestions, I performed four group calculations including PAW+dfpt, PAW+finite_electric_field, psp8+dfpt, and psp8+finite_electric_field for born effective charges and dielectric constant. The primitive cell is optimized sufficiently with large energy cutoff (800 eV) and larger k-mesh (16*16*16).

To summarize, dfpt cases with PAW and psp8 both give reasonable results, and psp8+finite_electric_field calculation also gives reasonable results though the berryphase_new warnings still exist. The calculation PAW+finite_electric_field gives reasonable dielectric constant but wrong born effective charges. The detailed results are attached with name data.out, as well as input file in PAW+finite_electricf_field calculation.

Currently I have not found available polarization data for GaN.

Regards,
Daosheng

Hi again Doasheng,

ok, so the warning is not the problem, the output is. It's very strange that the dielectric constant comes out ok (you get it from the P(E) curve?) but the Z* not... Can you compare the P(E) in the ncpp and PAW cases, as well as the P(R) ones? Could it be you are not in the linear regime wrt the atomic displacements R? Either too small R and numerical noise, or too large and nonlinear.

The experimental data would be for spontaneous polarization - I don't know if GaN is ferroelectric, or if that phase is stable experimentally. Have you checked? P(Efield) is normally an increasing monotonic function but that doesn't say anything about the free energy Etotal(P).

PS: see https://iopscience.iop.org/article/10.1 ... /14/13/302 for instance for the spontaneous polarization of GaN

Dear Professor,

Thanks for your reply.

The polarization in PAW and psp8 are nearly the same especially for ionic part while slight difference exits for electronic part. I calculated dielectric constant from the P(E) curve following the tutorial https://docs.abinit.org/tutorial/ffield/. I also checked the forces on each atoms at finite electric field, which shows that forces on each atoms are different for PAW and psp8 cases. In PAW, it gives wrong forces according to the born effective charges. Is it possible that there is something wrong in unit conversion?

Sorry for that I don't know what the P(R) mean. Is it polarization with atomic displacements? I also performed calculation of born effective charges with finite atomic displacements, which shows correct results. Since psp8 cases show good results, the electric field strength may be not too large.

The wurtzite structure is stable for GaN, which I am sure for that. For wurtzite GaN, it should be OK now since correct results can be calculated from psp8 pp.

In my research, I also calculated zincblende GaN. Same error happens that born effective charges from finite electric field calculation at PAW case are wrong, as well as the forces on each atoms.
There are also another strange results in my calculations on zincblende GaN with conventional cell (psp8 for pp). From my understanding, total polarization should be summary of electronic part and ionic part. However, in output file (attached), there are:

" Polarization in cartesian coordinates (a.u.):
(the sum of the electronic and ionic Berry phase has been folded into [-1, 1])
Electronic berry phase: -0.408803502E-04 -0.408803504E-04 -0.408803508E-04
Ionic: -0.134969915E-01 -0.134969915E-01 -0.134969915E-01
Total: 0.134561112E-01 0.134561112E-01 0.134561112E-01"

which seems wrong for total polarization. If I manually calculate total polarization with electronic and ionic parts, correct dielectric constant can be obtained.

Thanks & regards,
Daosheng

Supplement for last post, zincblende GaN is polar crystal without spontaneous polarization.