[Wien] symmetry broken for Cccm

[Peter Blaha]

Dear Igor,

I looked into this subtle problem and came to the following conclusions:

a) There is nothing wrong with the code.

Calculations in

i)   I4/mmm (B-lattic, a a c),
ii)  Cccm (doubled unit cell, CXY, a*sqrt2,c,a*sqrt2)    and the
iii) Pma2 (primitive (again doubled) supercell, a+sqrt2,a*sqrt2,c)

yield total energies of E, 2E and 4E within microRy precision, identical 
charges, ....

b) with respect to band structures there seems to be a subtle difficulty 
in interpreting the back-folding, which occurs in these cases.

I attach two plots for only a small (not over crowded) E-window to make 
the effects more clear.
i) The first plot in the smallest cell (I4/mmm) shows the bands from 
Gamma-X, but shown actually from Gamma-AB(1/4,1/4,0) and X(labelled 
2AB)(1/2,1/2,0)-AB(1/4,1/4,0), because this is what you will see when 
backfolding the BZ in the larger cell.

ii) The other plot in Cmmc (doubled cell, rotated) shows the bands from 
C (0,0,1/2) - Gamma - A(1/2,0,0) - 2A(1,0,0).
Obviously, the results of C-Gamma agree with the backfolded bands of i) 
(after overlaying them and mirroring).
On the other hand, out of the 4 bands C-Gamma, only the 1st and 4th of 
Gamma-A agree, while the other two disagree.
However, if I continue in this direction up to 2A, I can find in A-2A 
the 2 "missing bands".
So actually the C-Gamma direction is equivalent to Gamma-2A, but the 
latter also contains some other backfolded direction of the original 
I4/mmm cell (which I'm too lazy to identify ...)

So obviously, backfolding in these various centered cells is more 
difficult, but for sure consistently included.

Best regards
Peter

On 06/27/2017 08:31 PM, mazin wrote:
> Hi,
>
> I am running a pretty standard calculation for the BaFe2As2
> superconductor; have done zillions of those before. For testing
> purposes, I wanted to plot bands for the double-cell AF structure
> (.struct attached), but for the nonmagnetic case and, again, I do think
> I did the same before with no problems. Now I am using the 14.2, and it
> may be that I had used other versions before.
> Without magnetism, this structure is equivalent to I4/mmm (and WIEN2k
> does find this symmetry, if both Fe are made equivalent), so the
> resulting band must, up to numerical noise, possess full tetragonal
> symmetry. Yet, the bands along Gamm-X and Gamm-Y are noticeably
> different (note that in this setting X=(1,0,0), but Y=(0,0,1)).
> If I use the conventional cell (doubled, Pccm), the resulting bands have
> proper symmetry - even though the underlying unit cell is orthorhombic.
> So, the problem appears if the cell is base-centered.
>
> Thanks!
>
>
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-- 

                                       P.Blaha
--------------------------------------------------------------------------
Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
WWW:   http://www.imc.tuwien.ac.at/TC_Blaha
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