strange kinks/dicontinuities in GW band structure

[Boubacar Traore]

Hi all,

I have performed a G0W0 band structure calculation on a small cubic system with 44 electrons. I am using abinit as mean-field code.

After epsilon and sigma steps, I calculated the interpolated band structure using inteqp.cplx.x as in the attached image.

What I find strange is the different kinks/discontiniuities (shown by arrows in the image) in the GW band structure.

I must say that I am only adding few empty bands at this stage and the quasi-particle energies are surely not well converged but I just wanted to see the shape of the band structure.

Could you please enlighten me about what this may be due to? or if I am missing something?

Best,

Boubacar

[Zhenglu Li]

Hi Boubacar,

Your coarse kpoints may not be dense enough to have good interpolation.  You may try to include more kpoints in the Sigma step.  Wannier interpolation is another option (sig2wan.x utility).

Best,

Zhenglu

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[Boubacar Traore]

Hi Zhenglu,

Thank you for the reply.

I am using a 6x6x6 k-grid (lattice constant of 5.83Ang) generated with kgrid.x (during 2.1-wfn step as in Si tutorial) which I feed into sigma.inp. This grid should be sufficient for this system. However,  because of the symmetry of the system, the k-points have different weights. But, in my sigma.inp, I set all the scaling factors to 1.0, could that be  the problem as shown below?

---- kgrid.out during 2.1-wnf (mean-field calculation) ------

K_POINTS crystal
   20
  0.000000000  0.000000000  0.000000000   1.0
  0.000000000  0.000000000  0.166666667   6.0
  0.000000000  0.000000000  0.333333333   6.0
  0.000000000  0.000000000  0.500000000   3.0
  0.000000000  0.166666667  0.166666667  12.0
  0.000000000  0.166666667  0.333333333  24.0
  0.000000000  0.166666667  0.500000000  12.0
  0.000000000  0.333333333  0.333333333  12.0
  0.000000000  0.333333333  0.500000000  12.0
  0.000000000  0.500000000  0.500000000   3.0
  0.166666667  0.166666667  0.166666667   8.0
  0.166666667  0.166666667  0.333333333  24.0
  0.166666667  0.166666667  0.500000000  12.0
  0.166666667  0.333333333  0.333333333  24.0
  0.166666667  0.333333333  0.500000000  24.0
  0.166666667  0.500000000  0.500000000   6.0
  0.333333333  0.333333333  0.333333333   8.0
  0.333333333  0.333333333  0.500000000  12.0
  0.333333333  0.500000000  0.500000000   6.0
  0.500000000  0.500000000  0.500000000   1.0

----------------------------

And

----  kgrid fed into sigma.inp ---------

begin kpoints
  0.000000000  0.000000000  0.000000000  1.0
  0.000000000  0.000000000  0.166666667  1.0
  0.000000000  0.000000000  0.333333333  1.0
  0.000000000  0.000000000  0.500000000  1.0
  0.000000000  0.166666667  0.166666667  1.0
  0.000000000  0.166666667  0.333333333  1.0
  0.000000000  0.166666667  0.500000000  1.0
  0.000000000  0.333333333  0.333333333  1.0
  0.000000000  0.333333333  0.500000000  1.0
  0.000000000  0.500000000  0.500000000  1.0
  0.166666667  0.166666667  0.166666667  1.0
  0.166666667  0.166666667  0.333333333  1.0
  0.166666667  0.166666667  0.500000000  1.0
  0.166666667  0.333333333  0.333333333  1.0
  0.166666667  0.333333333  0.500000000  1.0
  0.166666667  0.500000000  0.500000000  1.0
  0.333333333  0.333333333  0.333333333  1.0
  0.333333333  0.333333333  0.500000000  1.0
  0.333333333  0.500000000  0.500000000  1.0
  0.500000000  0.500000000  0.500000000  1.0
end

--------------

Best,

Boubacar

[Zhenglu Li]

Hi Boubacar,

Yes, the scaling factor should be 1.0 regardless of k-points of weights.  You may try 1) increasing kpoints, 2) increase the number of coarse bands in the interpolation.  If all these don't work, it could be an indication that for your system GW correction is too large and reorders significantly the bands, and the wavefunction characters may need to be updated.

Best,

Zhenglu

[Boubacar Traore]

Hi Zhenglu,

I suspect the number of coarse  bands since I only used few (40 at the conduction band). I will try to increase that and see.

Just one precision: the quasi-particle energies for the added coarse bands need to have been calculated at the sigma step for inteqp to work, no?

Best,

Boubacar

[Zhenglu Li]

Hi Boubacar,

I was referring to "number_val_bands_coarse" and "number_cond_bands_coarse" in the inteqp.x input, and you should make them larger than those for the corresponding num_xxx_fine.  The number of empty bands in sigma in general only change the quasiparticle energies, and does not directly affect the interpolation step.  You don't need 40 bands for  "number_val_bands_coarse" in inteqp.x.  For any states you include for the  "number_val_bands_coarse" and "number_cond_bands_coarse" flags, they must have been calculated by sigma.

Best,

Zhenglu

[Boubacar Traore]

Hi Zhenglu,

Thanks!

I did the interpolation with only 2 for number_val_bands_fine and 2 for number_cond_bands_fine while keeping number_val_bands_coarse=22 and number_cond_bands_coarse=40, the GW bands for those 2 bands are much better but I can still see slight kinks (attached image)... What could this be still due to?  increasing number_xxx_bands_fine makes it worse.

Best,

Boubacar

[Zhenglu Li]

Hi Boubacar,

You can change number_val_bands_coarse and number_cond_bands_coarse to be to the order of 5, i.e. just a few more than the fine bands.  Also, make sure, your previous step sigma calculation have computed the  number_val_bands_coarse and number_cond_bands_coarse you set up in inteqp.

Best,

Zhenglu

[Boubacar Traore]

Hi Zhenglu,

Using 4 (or 5) for number_val_bands_coarse and number_cond_bands_coarse did not bring much change except that it slighly removed the disconituity at 7 eV between Gamma-X (smoother in lda band structure).

Do you have any rule of thumb for selecting these values  with regards to ratios etc.?

Just to be clear: could you confirm that number_val_bands_coarse (cond), is the number of bands counting down from VB maximum (or counting up from CB minimum to the specified value)?

Best,

Boubacar

[Zhenglu Li]

Hi Boubacar,

Generally making num_xxx_coarse a few more bands than num_xxx_fine would be good enough.  Both num_val and num_cond are counting from the gap, i.e. from VBM/CBM respectively.  This is consistent with BSE setup.

If this doesn't work, you can try what I mentioned earlier, by increasing coarse kpoints, or Wannier interpolation.  If they still don't work, it indicates your system is a difficult system which needs some wavefunction selfconsistency updates.

Best,

Zhenglu

[Boubacar Traore]

H Zhenglu,

Thanks for these information and your help.

I think that the way  num_xxx_coarse are counted for VB/CB should be explicitly stated in the manual since I find the current formulation a bit ambigous.

Ok, I will do more converged/refined tests to see . But from the literature, G0W0 appears to be sufficient for reasonable band structures. I guess, the kinks/disconitnuities that I see in my first post are more related to my previously unsuitable choices of number_xxx_bands_coarse and number_xxx_bands_fine values.

Best,

Boubacar

[Wenqi Yang]

Hi  Boubacar,

May I get to know whether you have solve this problem? I meet the same problem as you described. 

Best,

Wenqi