[Wien] optics broken symmetry

[Oleg Rubel]

Dear Peter, Laurence, and Xavier:

many thanks for looking into this issue and making suggestions.

The future plan is to go to 128+ atoms supercell for alloys. So the 
computational efficiency will be important at that point.

I also tried to eliminate all symmetry operations except for 
translation, of course. The structure file is at the bottom. There are 
some promising results obtained on a course k-grid.

k-mesh 8x8x8 not shifted, 1 symmetry operation

[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  0.906000E+01  0.930282E-01  0.906003E+01  0.930290E-01
    0.040820  0.906072E+01  0.943965E-01  0.906076E+01  0.943973E-01
    0.068030  0.906217E+01  0.958009E-01  0.906220E+01  0.958016E-01

k-mesh 8x8x8 shifted, 1 symmetry operation

[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  0.869517E+01  0.842315E-01  0.869517E+01  0.842315E-01
    0.040820  0.869576E+01  0.853542E-01  0.869576E+01  0.853542E-01
    0.068030  0.869695E+01  0.865021E-01  0.869695E+01  0.865021E-01

It seems that both shifted and unshifted mesh could work. I lean toward 
an unsifted mesh since the direct gap is at Gamma, so I would prefer to 
have it in the k-mesh. Even without symmetry 16x16x16 mesh might be more 
computationally efficient than the high-density mesh? The alloy 
structure will likely to have no symmetry either.

Going forward, I can try to see how far should the symmetry be reduced. 
Next candidate can be a face-centered orthorhombic structure. Any other 
thoughts?


Best regards
Oleg

P.S. Here is the structure file

[oleg at feynman InP-w2k]$ cat InP-w2k.struct
InP
F   LATTICE,NONEQUIV.ATOMS:  2
MODE OF CALC=RELA unit=ang
  11.090240 11.090240 11.090240 90.000000 90.000000 90.000000
ATOM  -1: X=0.00000000 Y=0.00000000 Z=0.00000000
           MULT= 1          ISPLIT= 8
In         NPT=  781  R0=0.00001000 RMT=    2.0000   Z: 49.000
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                      0.0000000 1.0000000 0.0000000
                      0.0000000 0.0000000 1.0000000
ATOM  -2: X=0.25000000 Y=0.25000000 Z=0.25000000
           MULT= 1          ISPLIT= 8
P          NPT=  781  R0=0.00010000 RMT=    2.0000   Z: 15.000
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                      0.0000000 1.0000000 0.0000000
                      0.0000000 0.0000000 1.0000000
    1      NUMBER OF SYMMETRY OPERATIONS
  1 0 0 0.00000000
  0 1 0 0.00000000
  0 0 1 0.00000000
        1

On 2018-09-05 06:10, Peter Blaha wrote:
> 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
>>
>