Questions on phonon degeneracy?

[yeyaokun]

Dear EPW Developers and Users,
Hi. I have some questions on phonon degeneracy and the EPW output results. Here's my situation.
I calculated an AlAs system with 2 atoms in its unit cell. I followed the process EPW provided to run the code, namely scf, nonscf, phonon and epw. And each step ended successfully without any program error. Then I got ele-ph matrix on coarse mesh by reading file alas.epb1, the file that stores the ele-ph matrix on coarse mesh according to EPW source code. When I checked the EPW results on coarse mesh(4*4*4 k points and 4*4*4 q points in my case), I found there's a dismatch in degeneracy on phonon branch and ele-ph matrix. As you can see in Fig 1, the ele-ph matrix shows a three-fold degeneracy on band m=n=1,k=1(0,0,0) , b=1-6(b for phonon brance), q=2(0,0,-0.25). But the alas.dyn2, the file that stores the phonon information on q=2, shows that the phonon branches should be two-fold degenerate, which can be seen in Fig 2.
Here's my question: the phonon branches only show two-fold degeneracy, why the ele-ph matrix shows three-fold degeneracy ? Do I understand the EPW results correctly? Or is there anything I got wrong? I would appreciate it if you can help me understand this. For your reference, I also uploaded my input files, in case there's anything wrong.
Looking forward to your reply. Thanks a lot.

Yaokun Ye
Ph.D Candidate from Peking University Shenzhen Graduate School.

Fig 1
m n k b q REAL PART IMA PART REAL**2+IMA**2
1 1 1 1 2 0.00779858 -0.03647151 0.00139099
1 1 1 2 2 0.00779858 -0.03647151 0.00139099
1 1 1 3 2 -0.00779858 0.03647151 0.00139099
1 1 1 4 2 0.04084267 0.03582770 0.00295175
1 1 1 5 2 0.04084264 0.03582768 0.00295174
1 1 1 6 2 -0.04084266 -0.03582767 0.00295175

Fig 2
**************************************************************************
freq ( 1) = 1.716893 [THz] = 57.269389 [cm-1]
( 0.568443 -0.002332 -0.388001 -0.006058 0.180442 -0.008390 )
( 0.560777 0.023770 -0.382417 -0.023770 0.178360 0.000000 )
freq ( 2) = 1.716893 [THz] = 57.269389 [cm-1]
( -0.119370 0.013434 -0.432241 0.012215 -0.551611 0.025648 )
( -0.118354 0.007776 -0.426890 -0.007776 -0.545245 0.000000 )
freq ( 3) = 4.508202 [THz] = 150.377446 [cm-1]
( -0.239043 0.384982 -0.239043 0.384982 0.239043 -0.384982 )
( -0.357743 -0.000000 -0.357743 -0.000000 0.357743 0.000000 )
freq ( 4) = 11.014391 [THz] = 367.400530 [cm-1]
( -0.248547 -0.015087 0.221975 0.016323 -0.026572 0.001236 )
( 0.696247 0.074849 -0.621440 -0.074849 0.074807 0.000000 )
freq ( 5) = 11.014391 [THz] = 367.400530 [cm-1]
( 0.112998 -0.007857 0.158969 -0.004788 0.271967 -0.012646 )
( -0.318460 0.007313 -0.447201 -0.007313 -0.765661 0.000000 )
freq ( 6) = 11.807806 [THz] = 393.866005 [cm-1]
( -0.083285 0.134132 -0.083285 0.134132 0.083285 -0.134132 )
( 0.555343 0.000000 0.555343 0.000000 -0.555343 0.000000 )
**************************************************************************

[sponce]

Dear Yaokun Ye,

Thank you for your interest in EPW and welcome to the forum.

It seems you are looking at the change of potential on the real-space grid (something similar to a deformation potential) and not the
electron-phonon matrix element. From your Fig.1 you can see that the real part and imaginary part respect the phonon mode degeneracy (2,1,2,1).

You can try printing the electron-phonon matrix elements using the "prtgkk" input keyword.
If you want it on the coarse grid, just use the same fine grid as the coarse grid.
In that case the phonon frequency will be included at the denominator such that I expect you will get the correct degeneracy as well.

Best wishes,
Samuel

[yeyaokun]

Dear Dr Samuel Poncé,

Thanks a lot for your kindly reply. I'll try your advice and check more things by myself first.

Best wishes.

Yaokun Ye

[hlee]

Dear Yaokun Ye:

The electron-phonon matrix elements stored in prefix.epb* files are given in terms of the Cartesian representation, (NOT the mode representation).
This means the first mode index in Fig 1 doesn't match the first mode index in Fig 2; the first mode index in Fig 1 represents the x component of the atom with the first species index.

Therefore, your comparison is not meaningful.

Regarding the conversion between the mode and the Cartesian representation, please look at the subroutines of rotate_eigenm and rotate_epmat in the file of rotate.f90 (https://gitlab.com/QEF/q-e/-/blob/devel ... rotate.f90).

Sincerely,

H. Lee