Unexpected affect of coarse q-grid on electronic energies

[Vahid]

Dear EPW Users,

I am working on tin selenide orthorhombic structure, which is a polar material. A 4x12x12 k-grid adequately reproduces the electronic band structure between the QE and the Wannier90 codes.

When attempting to plot the electronic band structure with EPW-6.0, I use 4x12x12 for the coarse k-grid. For the fine k-grid, I use the band structure segments in the BZ. I found that by changing the q-grids, the wannier-interpolated electronic energies change. Using q-grids of 1x3x3 or 2x6x6 reproduces the correct electronic energies. But q-grids (both coarse and fine) of 4x6x6 lower the VBM by ~14meV. Attached are the band structure plots for two q-grids (https://drive.google.com/file/d/0B_CotT ... sp=sharing). BTW, to reproduce the QE phonon band structure, I would need at least a 4x6x6 coarse q-grid.

Is there any reason why the size of the q-grids should affect the electronic energies? I printed some of the variables used in energy interpolation and found some differences between the rotation matrices (cufkk) between the two q-grids (2x6x6 and 4x6x6). Somehow, I think the electronic energies should be independent of the q-grids but I may be wrong.

Thank you,

Vahid

Vahid Askarpour
Department of Physics and Atmospheric Science
Dalhousie University,
Halifax, NS, Canada

[carla.verdi]

Dear Vahid,

You are correct, the interpolation of just the electronic eigenvalues should be independent of the q grid, i.e. of the phonons.
Did you run epw with exactly the same inputs, just different coarse q grids? and the same scf/nscf calculation before? Are the Wannier function centers and spreads printed in the epw output the same?

Best,
Carla

[Vahid]

Dear Carla,

Yes, the scf.in, nscf.in and epw.in files are identical except for the q-grids and the save file for phonons. The wannier centres and spreads are the same. I even used the same number of cpus for the two runs. I would be happy to send you all the input and output files for the two q-grids if necessary.

Thanks,

Vahid

[Vahid]

Dear Carla,

I came up with a 15-minute test that demonstrates the effect of q-grid on electronic energies. I used the MgB2 t05 test case and set

elecselfen = .true.

I used a 4x4x4 fine and coarse k-grids in both tests.

In test1, I used a coarse and fine q-grid of 2x2x4. In test2, I used a coarse and fine q-grid of 4x4x4.

Here are the energies for the Gamma point:

Code: Select all

The wannier centres and spreads are identical for the two cases

     (  -0.00000   0.57735   0.41448) :   2.05205
     (   0.50000   0.28868   0.41448) :   2.05205
     (   0.00000   0.86603   0.65623) :   1.16844
     (  -0.25000   0.43301   0.65623) :   1.16844
     (   0.25000   0.43301   0.65623) :   1.16844

For q-grids=2x2x4

     ik =       1 coord.:    0.0000000   0.0000000   0.0000000
     -------------------------------------------------------------------
     E(   3 )=   0.2904 eV   Re[Sigma]=    -111.236280 meV Im[Sigma]=     281.893635 meV     Z=       1.679479 lam=      -0.404577
     E(   4 )=   0.2909 eV   Re[Sigma]=    -118.220302 meV Im[Sigma]=     260.586096 meV     Z=       1.317733 lam=      -0.241121
     E(   5 )=   7.7831 eV   Re[Sigma]=      11.509445 meV Im[Sigma]=       0.421644 meV     Z=       1.000130 lam=      -0.000130

For q-grids=4x4x4
     ik =       1 coord.:    0.0000000   0.0000000   0.0000000
     -------------------------------------------------------------------
     E(   3 )=   0.1324 eV   Re[Sigma]=     -40.945190 meV Im[Sigma]=      92.580247 meV     Z=       1.111982 lam=      -0.100705
     E(   4 )=   0.1324 eV   Re[Sigma]=     -40.945190 meV Im[Sigma]=      92.580247 meV     Z=       1.111982 lam=      -0.100705
     E(   5 )=   7.8852 eV   Re[Sigma]=      24.783399 meV Im[Sigma]=      12.615568 meV     Z=       1.026825 lam=      -0.026124

Best,

Vahid

[sponce]

Dear Vahid,

The coarse k-point and q-point grid needs to be commensurate and the k-point grid needs to be larger or equal to the q-point grid.

So in your original problem:
4x12x12 k-grid
2x6x6 q grid
but not 4x6x6 q grid.

If you want to use a 4x6x6 q grid, you would need a 8x12x12 k grid (or a 4x6x6 k-grid).

This is because of the way the Wigner-Seitz cells are built.

Best,
Samuel

[Vahid]

Dear Samuel,

Thank you for this tip. I know the code stops if the grids are not commensurate. It also stops if the coarse q-grid is larger than the k-grid. However, it did not complain in my case because 4x6x6 is commensurate with 4x12x12 and it is equal or smaller than 4x12x12, in a way.

So now I know that nk1=m*nq1, nk2=m*nq2 and nk3=m*nq3 with the integer m being 1,2, etc.

Best,

Vahid