electron-phonon matrix elements

Theory Electron-phonon
1

Dear All,

I am a participant of ‘School on Electron-Phonon Physics from First Principles’ held at the International Centre for Theoretical Physics in Trieste on 19-23 March 2018. It was a very good school and I had a great experience attending the School.

On Tuesdays Hands-on section, we tried to compute the electron-phonon matrix elements using a slightly modified phonon program (which includes printing information). It seems like the output from those calculations are ‘|g(q-point, frequency, band1, band2)|’. The g-matrix should be a function of k-point also, which is missing in the output. I found on the subroutine ‘elphel’ it is mentioned that

write(6,)
write(6,) ‘We here write only the matrix elements for k=Gamma in the first proc:’
write(6,*)
!
! consider only initial state k=0

Does this mean that all the |g| written on the output file are for k=0? In this case how one can get |g| as s function of k-point as well.

Thank you for your time and consideration,
Best regards,
Fairoja.

Fairoja Cheenicode Kabeer
Postdoctoral researcher,
Materials Theory,
Uppsala University.

2

Dear Fairoja,

You can consider any state. We only show the el-ph matrix element at k=\Gamma and then changed q.
However you can look at any k-point.

In the code you have:
[code:zpn67iwv] ! consider only initial state k=0
ik = 1
WRITE(6,‘(a,3f10.6)’) 'xk ', (xk(n,ik),n=1,3)[/code:zpn67iwv]

where ik=1 is in this case the Gamma point. You can just change that value to get different k-points.
Note that you can also add k-point loop around all of that like this
[code:zpn67iwv]DO ik=1, MAX_NUMBER_OF_K_POINTS
WRITE(6,‘(a,3f10.6)’) 'xk ‘, (xk(n,ik),n=1,3)
write(6,*) ’ ibnd jbnd imode eig_i (eV) eig_j (eV) omega_nu (meV) |g| (meV)’
...
ENDDO[/code:zpn67iwv]

Be careful that this will generate very large txt files (lots of data).

Best wishes,
Samuel

3

Dear sponce,

I am interested in the same topic.

I downloaded the version released for the school
in the subroutine ‘./tests/Inputs/t07/elphon.f90’ there is
[code:1p94d4f9] ! consider only initial state k=0
ik = 2
WRITE(6,‘(a,3f10.6)’) 'xk ', (xk(n,ik),n=1,3)
![/code:1p94d4f9]
What does this ‘2’ represent?

how can i change it if I am interested in specific k point?
Thank you in advance for any help

Sara Fiore

ETH Zrich | PhD Student | Doctorate at D-ITET
Rechn. Modellierung Nanostrukturen

4

Dear Sara Fiore,

This is the specific k-point to be printed (ik=2 is the second k-point (of the local pool, so better to do this with 1 cpu)).
The k-point value (x,y,z coordinate) will be reported in the output with the line
WRITE(6,‘(a,3f10.6)’) 'xk ', (xk(n,ik),n=1,3)

Best,
Samuel

5

Dear Samual,

Thank you for the reply! I tried to modify the output writing part of the program (subroutine elphsum2 of elphon.f90) and performed some calculations. I have tried different q-points

q1 0.000000000000000 0.000000000000000 0.000000000000000
q2 0.000000000000000 0.000000000000000 0.119721397504348
q3 0.000000000000000 0.000000000000000 -0.239442795008697
q4 0.000000000000000 0.125000000000000 0.125000000000000 …

The first three finished without any issue, but the output file for the q4 has some NaN values written.

The following is the style of output

ibnd jbnd imode omega_nu (meV)

loop over k-points

|g| (meV) eig_i(k) (eV) eig_j(q) (eV)

end loop

  54.268873       0.000000       0.000000
  55.053020       0.000000       0.000000
  56.387030       0.000000       0.000000
        NaN       0.000000            NaN
  55.010279       0.000000       0.000000
  54.644403       0.000000       0.000000

…
4.733780 12316.262843 53834.825476
NaN 55197.660572 NaN
30.164047 0.000000 0.000000
30.031159 0.000000 0.000000
30.054339 0.000000 0.000000
59.273177*************** 0.000000
27.924379 0.000000 0.000000

Can you please comment on this issue. Is it due to the writing issue of eig_j(q)? if yes, How can I solve this?

Thank you very much for your time and consideration,
Fairoja.

Fairoja Cheenicode Kabeer
Postdoctoral researcher,
Uppsala University.

6

Dear Samuel,
thank you for your answer and I am sorry to have to ask again your help (and that I’m mixing my questions with the ones of the other user)

I do not understand : ik =2 is the second point of what? of a list? of a grid? which list/grid?
I am using the following inputs from the School : Hands-on 1: [i:3icmok2y]Electron-phonon matrix elements with EPW, polar materials –> Wed.4.tar[/i:3icmok2y]
In sic.epw.in : I tried to substitute to
[code:3icmok2y]
nkf1 = 1
nkf2 = 1
nkf3 = 1
[/code:3icmok2y]
the following
[code:3icmok2y]filkf = ‘k.dat’[/code:3icmok2y]

with
k.dat
[code:3icmok2y] 43
0.000000 0.000000 0.000000 1.0
0.000000 0.050000 0.050000 1.0
0.000000 0.100000 0.100000 1.0
0.000000 0.150000 0.150000 1.0
0.000000 0.200000 0.200000 1.0
0.000000 0.250000 0.250000 1.0
0.000000 0.300000 0.300000 1.0
0.000000 0.350000 0.350000 1.0
0.000000 0.400000 0.400000 1.0
0.000000 0.450000 0.450000 1.0
0.000000 0.500000 0.500000 1.0
0.050000 0.500000 0.550000 1.0
0.100000 0.500000 0.600000 1.0
0.150000 0.500000 0.650000 1.0
0.200000 0.500000 0.700000 1.0
0.250000 0.500000 0.750000 1.0
0.285714 0.500000 0.714286 1.0
0.321429 0.500000 0.678571 1.0
0.357143 0.500000 0.642857 1.0
0.392857 0.500000 0.607143 1.0
0.428571 0.500000 0.571429 1.0
0.464286 0.500000 0.535714 1.0
0.500000 0.500000 0.500000 1.0
0.444444 0.444444 0.444444 1.0
0.388889 0.388889 0.388889 1.0
0.333333 0.333333 0.333333 1.0
0.277778 0.277778 0.277778 1.0
0.222222 0.222222 0.222222 1.0
0.166667 0.166667 0.166667 1.0
0.111111 0.111111 0.111111 1.0
0.055556 0.055556 0.055556 1.0
0.000000 0.000000 0.000000 1.0
0.034091 0.034091 0.068182 1.0
0.068182 0.068182 0.136364 1.0
0.102273 0.102273 0.204545 1.0
0.136364 0.136364 0.272727 1.0
0.170455 0.170455 0.340909 1.0
0.204545 0.204545 0.409091 1.0
0.238636 0.238636 0.477273 1.0
0.272727 0.272727 0.545455 1.0
0.306818 0.306818 0.613636 1.0
0.340909 0.340909 0.681818 1.0
0.375000 0.375000 0.750000 1.0[/code:3icmok2y]
i.e. the same values of the file path.dat

I tried to run this [b:3icmok2y]modified version[/b:3icmok2y]
but I get the following result… ( no more dependence from q point exist from the second step on … )
[code:3icmok2y] Number of ep-matrix elements per pool : 264 ~= 2.06 Kb (@ 8 bytes/ DP)
Electron-phonon vertex |g| (meV)

 iq =       1 coord.:    0.0000000   0.0000000   0.0000000
 ik =       1 coord.:    0.0000000   0.0000000   0.0000000
  ibnd     jbnd     imode   enk[eV]    enk+q[eV] omega(q)[meV]   |g|[meV]

    1        1        1     -6.1066     -6.1066      0.0000 0.5222169534E-02
    1        1        2     -6.1066     -6.1066      0.0000 0.5222169534E-02
    1        1        3     -6.1066     -6.1066      0.0000 0.5222169534E-02
    1        1        4     -6.1066     -6.1066     95.9221 0.1275773102E-05
    1        1        5     -6.1066     -6.1066     95.9221 0.1275773102E-05
    1        1        6     -6.1066     -6.1066     95.9221 0.1275773102E-05
    1        2        1     -6.1066      9.3595      0.0000 0.2822526284E+06
    1        2        2     -6.1066      9.3595      0.0000 0.2822526284E+06
    1        2        3     -6.1066      9.3595      0.0000 0.2822526284E+06
    1        2        4     -6.1066      9.3595     95.9221 0.1568913091E+03
    1        2        5     -6.1066      9.3595     95.9221 0.1568913091E+03
    1        2        6     -6.1066      9.3595     95.9221 0.1568913091E+03
    2        1        1      9.3595     -6.1066      0.0000 0.2821764810E+06
    2        1        2      9.3595     -6.1066      0.0000 0.2821764810E+06
    2        1        3      9.3595     -6.1066      0.0000 0.2821764810E+06
    2        1        4      9.3595     -6.1066     95.9221 0.1568913091E+03
    2        1        5      9.3595     -6.1066     95.9221 0.1568913091E+03
    2        1        6      9.3595     -6.1066     95.9221 0.1568913091E+03
    2        2        1      9.3595      9.3595      0.0000 0.1071685442E+02
    2        2        2      9.3595      9.3595      0.0000 0.1071685442E+02
    2        2        3      9.3595      9.3595      0.0000 0.1071685442E+02
    2        2        4      9.3595      9.3595     95.9221 0.1263503597E+03
    2        2        5      9.3595      9.3595     95.9221 0.1263503597E+03
    2        2        6      9.3595      9.3595     95.9221 0.1263503597E+03

 ik =       2 coord.:    0.0000000   0.0500000   0.0500000
  ibnd     jbnd     imode   enk[eV]    enk+q[eV] omega(q)[meV]   |g|[meV]

    1        1        1     -6.0355     -6.0355      0.0000 0.5799412816E-02
    1        1        2     -6.0355     -6.0355      0.0000 0.5799412816E-02
    1        1        3     -6.0355     -6.0355      0.0000 0.5799412816E-02
    1        1        4     -6.0355     -6.0355     95.9221 0.1588303029E-05
    1        1        5     -6.0355     -6.0355     95.9221 0.1588303029E-05
    1        1        6     -6.0355     -6.0355     95.9221 0.1588303029E-05
    1        2        1     -6.0355      9.1560      0.0000 0.2776357961E+06
    1        2        2     -6.0355      9.1560      0.0000 0.2776357961E+06
    1        2        3     -6.0355      9.1560      0.0000 0.2776357961E+06
    1        2        4     -6.0355      9.1560     95.9221 0.1548695773E+03
    1        2        5     -6.0355      9.1560     95.9221 0.1548695773E+03
    1        2        6     -6.0355      9.1560     95.9221 0.1548695773E+03
    2        1        1      9.1560     -6.0355      0.0000 0.2776357961E+06
    2        1        2      9.1560     -6.0355      0.0000 0.2776357961E+06
    2        1        3      9.1560     -6.0355      0.0000 0.2776357961E+06

...
.... [/code:3icmok2y]

while with the [b:3icmok2y]unchanged sic.epw.in [/b:3icmok2y]I get

[code:3icmok2y] Number of ep-matrix elements per pool : 54 ~= 0.42 Kb (@ 8 bytes/ DP)
Electron-phonon vertex |g| (meV)

 iq =       1 coord.:    0.0000000   0.0000000   0.0000000
 ik =       1 coord.:    0.0000000   0.0000000   0.0000000
  ibnd     jbnd     imode   enk[eV]    enk+q[eV] omega(q)[meV]   |g|[meV]

    2        2        1      9.3595      9.3595      0.0000 0.1025382412E+02
    2        2        2      9.3595      9.3595      0.0000 0.1025382412E+02
    2        2        3      9.3595      9.3595      0.0000 0.1025382412E+02
    2        2        4      9.3595      9.3595     95.9221 0.1176469183E+03
    2        2        5      9.3595      9.3595     95.9221 0.1176469183E+03
    2        2        6      9.3595      9.3595     95.9221 0.1176469183E+03
    2        3        1      9.3595      9.3595      0.0000 0.1025382412E+02
    2        3        2      9.3595      9.3595      0.0000 0.1025382412E+02
    2        3        3      9.3595      9.3595      0.0000 0.1025382412E+02
    2        3        4      9.3595      9.3595     95.9221 0.1176469183E+03
    2        3        5      9.3595      9.3595     95.9221 0.1176469183E+03
    2        3        6      9.3595      9.3595     95.9221 0.1176469183E+03
    2        4        1      9.3595      9.3595      0.0000 0.1025382412E+02
    2        4        2      9.3595      9.3595      0.0000 0.1025382412E+02
    2        4        3      9.3595      9.3595      0.0000 0.1025382412E+02
    2        4        4      9.3595      9.3595     95.9221 0.1176469183E+03
    2        4        5      9.3595      9.3595     95.9221 0.1176469183E+03
    2        4        6      9.3595      9.3595     95.9221 0.1176469183E+03
    3        2        1      9.3595      9.3595      0.0000 0.1025382412E+02
    3        2        2      9.3595      9.3595      0.0000 0.1025382412E+02
    3        2        3      9.3595      9.3595      0.0000 0.1025382412E+02
    3        2        4      9.3595      9.3595     95.9221 0.1176469183E+03
    3        2        5      9.3595      9.3595     95.9221 0.1176469183E+03
    3        2        6      9.3595      9.3595     95.9221 0.1176469183E+03
    3        3        1      9.3595      9.3595      0.0000 0.1025382412E+02
    3        3        2      9.3595      9.3595      0.0000 0.1025382412E+02
    3        3        3      9.3595      9.3595      0.0000 0.1025382412E+02
    3        3        4      9.3595      9.3595     95.9221 0.1176469183E+03
    3        3        5      9.3595      9.3595     95.9221 0.1176469183E+03
    3        3        6      9.3595      9.3595     95.9221 0.1176469183E+03
    3        4        1      9.3595      9.3595      0.0000 0.1025382412E+02
    3        4        2      9.3595      9.3595      0.0000 0.1025382412E+02
    3        4        3      9.3595      9.3595      0.0000 0.1025382412E+02
    3        4        4      9.3595      9.3595     95.9221 0.1176469183E+03
    3        4        5      9.3595      9.3595     95.9221 0.1176469183E+03
    3        4        6      9.3595      9.3595     95.9221 0.1176469183E+03
    4        2        1      9.3595      9.3595      0.0000 0.1025382412E+02
    4        2        2      9.3595      9.3595      0.0000 0.1025382412E+02
    4        2        3      9.3595      9.3595      0.0000 0.1025382412E+02
    4        2        4      9.3595      9.3595     95.9221 0.1176469183E+03
    4        2        5      9.3595      9.3595     95.9221 0.1176469183E+03
    4        2        6      9.3595      9.3595     95.9221 0.1176469183E+03
    4        3        1      9.3595      9.3595      0.0000 0.1025382412E+02
    4        3        2      9.3595      9.3595      0.0000 0.1025382412E+02
    4        3        3      9.3595      9.3595      0.0000 0.1025382412E+02
    4        3        4      9.3595      9.3595     95.9221 0.1176469183E+03
    4        3        5      9.3595      9.3595     95.9221 0.1176469183E+03
    4        3        6      9.3595      9.3595     95.9221 0.1176469183E+03
    4        4        1      9.3595      9.3595      0.0000 0.1025382412E+02
    4        4        2      9.3595      9.3595      0.0000 0.1025382412E+02
    4        4        3      9.3595      9.3595      0.0000 0.1025382412E+02
    4        4        4      9.3595      9.3595     95.9221 0.1176469183E+03
    4        4        5      9.3595      9.3595     95.9221 0.1176469183E+03
    4        4        6      9.3595      9.3595     95.9221 0.1176469183E+03

  Electron-phonon vertex |g| (meV)

 iq =       2 coord.:    0.0000000   0.0500000   0.0500000
 ik =       1 coord.:    0.0000000   0.0000000   0.0000000
  ibnd     jbnd     imode   enk[eV]    enk+q[eV] omega(q)[meV]   |g|[meV]

    2        2        1      9.3595      9.1560      7.3642 0.1410651751E+02
    2        2        2      9.3595      9.1560      7.4177 0.7448860647E+01
    2        2        3      9.3595      9.1560     10.6462 0.2261395359E+02
    2        2        4      9.3595      9.1560     95.7931 0.1457131275E+03
    2        2        5      9.3595      9.1560     95.7938 0.1457131275E+03
    2        2        6      9.3595      9.1560    116.0048 0.5846914499E+03
    2        3        1      9.3595      9.2361      7.3642 0.2127339868E+02
    2        3        2      9.3595      9.2361      7.4177 0.4533876775E+01
    2        3        3      9.3595      9.2361     10.6462 0.4948183599E+02
    2        3        4      9.3595      9.2361     95.7931 0.1023130164E+03
    2        3        5      9.3595      9.2361     95.7938 0.1023130164E+03
    2        3        6      9.3595      9.2361    116.0048 0.6042865706E+03
    2        4        1      9.3595      9.2361      7.3642 0.2127339868E+02 [/code:3icmok2y]

let us assume that I am interested to compute[b:3icmok2y] g((0.272727 , 0.272727 , 0.545455) ; q)[/b:3icmok2y]

I really don’t understand how to do that.

I am sorry for such a long post and I thank you in advance for all your time and consideration

Bests
Sara

7

Hi Sara,

ik = 2 is the second k-point in the grid (if you provide a mesh) or in the list (if you provide a file with the path).

The point you listed 0.272727 0.272727 0.545455 would be ik=40 in the k.dat list provided.

Best,
Roxana