[Pw_forum] different results for electron-phonon calculation for the same q-point

[Florian Rittweger]

Dear all,

I calculate the electron-phonon coupling strength for bulk aluminum with 
QE V.5.1, using two grids of q-points - 222 and 444. Looking at a 
specific q-point which is contained in both grids, namely q = (0.0, 
-1.0, 0.0), the results for the electron-phonon coefficient lambda and 
the linewidth gamma differs. Additionally i did the electron-phonon 
calculation for the single q-point with ldisp=.false., yielding 
different results as well.

electron-phonon input:

222-Q-POINT-GRID
  &inputph
   ...
   ldisp=.true.
   nq1=2, nq2=2, nq3=2
  /

444-Q-POINT-GRID
  &inputph
   ...
   ldisp=.true.
   nq1=4, nq2=4, nq3=4
  /

SINGLE Q-POINT
  &inputph
   ...
   ldisp=.false.
  /
0.000 -1.000 0.000

The flags electron_phonon='interpolated', trans=.true., 
el_ph_sigma=0.005 and el_ph_nsigma=1 are used in all calculations.

electron-phonon output:

222-Q-POINT-GRID

  Calculation of q =    0.0000000  -1.0000000   0.0000000
  ...
  **************************************************************************
      freq (    1) =       4.913252 [THz] =     163.888446 [cm-1]
      freq (    2) =       4.913252 [THz] =     163.888446 [cm-1]
      freq (    3) =      10.206764 [THz] =     340.461002 [cm-1]
  **************************************************************************
      Mode symmetry, D_4h(4/mmm) point group:
      freq (  1 -  2) =        163.9  [cm-1]   --> E_u  X_5' M_5'
      freq (  3 -  3) =        340.5  [cm-1]   --> A_2u X_4' M_4'
      electron-phonon interaction  ...
      Gaussian Broadening:   0.005 Ry, ngauss=   0
      DOS =  5.347024 states/spin/Ry/Unit Cell at Ef=  8.438471 eV
      lambda(    1)=  1.4445   gamma=  178.06 GHz
      lambda(    2)=  1.1812   gamma=  145.60 GHz
      lambda(    3)=  0.3285   gamma=  174.76 GHz

444-Q-POINT-GRID

  Calculation of q =    0.0000000  -1.0000000   0.0000000
  ...
  **************************************************************************
      freq (    1) =       4.913092 [THz] =     163.883106 [cm-1]
      freq (    2) =       4.913092 [THz] =     163.883106 [cm-1]
      freq (    3) =      10.205145 [THz] =     340.406980 [cm-1]
  **************************************************************************
      Mode symmetry, D_4h(4/mmm) point group:
      freq (  1 -  2) =        163.9  [cm-1]   --> E_u  X_5' M_5'
      freq (  3 -  3) =        340.4  [cm-1]   --> A_2u X_4' M_4'
      electron-phonon interaction  ...
      Gaussian Broadening:   0.005 Ry, ngauss=   0
      DOS =  5.347024 states/spin/Ry/Unit Cell at Ef=  8.438471 eV
      lambda(    1)=  1.0271   gamma=  126.59 GHz
      lambda(    2)=  1.5098   gamma=  186.09 GHz
      lambda(    3)=  0.4284   gamma=  227.80 GHz

SINGLE Q-POINT

  Calculation of q =    0.0000000  -1.0000000   0.0000000
  ...
  **************************************************************************
      freq (    1) =       4.913143 [THz] =     163.884808 [cm-1]
      freq (    2) =       4.913143 [THz] =     163.884808 [cm-1]
      freq (    3) =      10.206794 [THz] =     340.462013 [cm-1]
  **************************************************************************
      Mode symmetry, D_4h(4/mmm) point group:
      freq (  1 -  2) =        163.9  [cm-1]   --> E_u  X_5' M_5'
      freq (  3 -  3) =        340.5  [cm-1]   --> A_2u X_4' M_4'
      electron-phonon interaction  ...
      Gaussian Broadening:   0.005 Ry, ngauss=   0
      DOS =  5.347024 states/spin/Ry/Unit Cell at Ef=  8.438471 eV
      lambda(    1)=  1.2835   gamma=  158.19 GHz
      lambda(    2)=  1.2835   gamma=  158.19 GHz
      lambda(    3)=  0.3946   gamma=  209.89 GHz


The dynamical matrices are equal in all three cases but the eigenvectors 
(and therefor the values for lambda and gamma?) differ with respect to 
direction and/or magnitude.
As far as i thought all three calculations should give the same results. 
Is there an explanation why this shoudn't be true?

Any hints, discussion or explanation would be helpful.

With best regards,
Florian


-------------------------------------------------------------
Florian Rittweger, PhD student
Max Planck Institute of Microstructure Physics
Von-Seckendorff-Platz 1, Room 1.07
D-06120 Halle/Saale, Germany
Tel.: ++49 345 5525462
-------------------------------------------------------------