[Wien] optics broken symmetry

[Peter Blaha]

Dear Oleg,

I looked into the problem and unfortunately I can offer only a partial 
solution. I confirm that:

a) The scf cycle gives identical results with or without broken symmetry.

b) The optics gives "wrong" results with broken symmetry.

I inspected the matrix elements and the problem seems to be with 
degenerate states (eg. the VBM is 3 fold degenerate at Gamma).

The corresponding momentum matrix elements in cubic case are all the 
same (for all 3 eigenvalues and all directions, i.e. Mxx=Myy=Mzz and 
M10_13 = M11_13 = M_12_13, where the numbers indicate the band indices 
of the transition).
In the non-cubic setup, they are NOT the same, but in my opinion they 
are still correct (If you sum over the 3 eigenvalues 10-12, you get the 
same result as in the cubic one, but individually I get (for distortions 
in z, not in x as you did) M_10_13: (0 0 zz); M_11_13 (zz/2 zz/2 0) and 
the same for M_12_13, while in cubic all 3 matrix elements are (zz/3 
zz/3 zz/3).
So I concluded the problem is in the tetrahedron method used in joint. 
However, I was not able to find a "bug" in SRC_joint. It seems to be 
inherent to the method.

The partial fix: Do it "brute force", i.e. increase the number of 
k-points until convergence: For instance with k-meshes of
          27 27 27  eps1-xx/zz(0.0136eV)   0.117709E+02 0.117134E+02
          34 34 34                         0.118539E+02 0.118216E+02
200000k (58 58 58):                       0.119641E+02 0.119573E+02

200000k cubic setup:                      0.119618E+02 0.119618E+02

Obviously, the error in the tetrahedron method due to degenerate 
eigenvalues (like at Gamma or other high symmetry points) is reduced the 
more "general k-points" are in the mesh and the result converges towards 
the cubic result. In addition, eps-1(0) changes anyway from 11.7 to 11.9 
with these k-meshes, so are not yet fully converged.

In terms of cpu-time at least for such cells it is not really a problem 
to use a 100 100 100 grid (or more).

Best regards
Peter

On 09/03/2018 05:33 AM, Oleg Rubel wrote:
> Dear Wien2k community,
> 
> I try to compute opto-elastic properties of InP (zinc-blend structure). 
> It is related to a change of the dielectric constant (real part) in 
> response to an applied strain. There are no problems with a response to 
> a hydrostatic strain, and results agree well with experiments. A problem 
> occurs with a uniaxial strain (strained along X-axis only by 0.05%). 
> Computed change in the dielectric constant is too large (~ an order of 
> magnitude).
> 
> Trying to trace back the problem, I did the following:
> First, I initialize a tetragonaly-distorted zinc-blend structure 
> (init_lapw -b -vxc 19 -ecut -6.5 -numk 800) with the following lattice 
> parameters
> 
> F   LATTICE,NONEQUIV.ATOMS:  2
> MODE OF CALC=RELA unit=ang
>   11.095785 11.090240 11.090240 90.000000 90.000000 90.000000
> 
> Then I set the lattice parameters back to the cubic lattice
> 
> F   LATTICE,NONEQUIV.ATOMS:  2
> MODE OF CALC=RELA unit=ang
>   11.090240 11.090240 11.090240 90.000000 90.000000 90.000000
> 
> and rerun (x dstart). This allows me to preserve the symmetry of a 
> distorted structure (see the structure file below).
> 
> Next, I run SCF (run_lapw -ec 0.00001 -cc 0.0001) and optics with 
> 20x20x20 k-mesh. The results for Re and Im parts of the dielectric 
> constant are here:
> 
> [oleg at feynman InP-w2k]$ head InP-w2k.epsilon
> #
> # Lorentzian broadening with gamma= 0.100000  [eV]
> # Im(epsilon) shifted by   0.7860   [eV]
> # No intraband contributions added
> #
> # Energy [eV] Re_eps_xx     Im_eps_xx     Re_eps_yy     Im_eps_yy
> #
>     0.013610  0.940850E+01  0.988634E-01  0.947674E+01  0.100908E+00
>     0.040820  0.940928E+01  0.100340E+00  0.947756E+01  0.102453E+00
>     0.068030  0.941084E+01  0.101855E+00  0.947919E+01  0.104042E+00
> 
> It seems that the symmetry is broken, which causes later problems with 
> opto-elastic coefficients as change of 0.07 in the second decimal point 
> of Re_eps for such a small strain is too much.
> 
> Once again, there are no problems when the strain tensor does not break 
> the zinc-blend cubic symmetry.
> 
> Any thoughts are highly appreciated.
> 
> 
> Thank you in advance
> Oleg
> 

-- 

                                       P.Blaha
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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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