EPW phonon linewidth inconsistent with QE results

[zz11ss11zz]

Dear all,

Recently, I try to use EPW to study CDW property. The bandstructure and phonon dispersion are perfect agree with the QE results. But their linewidth of the lowest phonon has large differences.

phonon linewidth.png (42.73 KiB) Viewed 6510 times

Is this a normal phenomenon because EPW has more dense k/q points than QE? I put my input in the following:

QE input:
scf0.in

Code: Select all

 &control
    calculation='scf',
    prefix='TaSe2',
    pseudo_dir = '/home/users/nus/e0338235/pseudo/sg15_oncv_upf_2020-02-06',
    outdir='./tmp'
    tstress = .true.,
    tprnfor = .true., 
   etot_conv_thr=1.0D-7
   forc_conv_thr=4.0D-6
/
 &system
    a     =  3.50078e+00
    c     =  1.81000e+01
   ibrav = 4, nat=3, ntyp=2,
    ecutwfc = 80.0
!    ecutrho = 800.0
   occupations='smearing', smearing='fd', degauss=0.005
   la2f=.true.
/
 &electrons
    mixing_beta = 0.7
    conv_thr =  1.0d-10
 /
ATOMIC_SPECIES
Ta  180.947   Ta_ONCV_PBE-1.2.upf
Se   78.96    Se_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS {angstrom}
Ta       0.000000   0.000000   0.000000
Se      1.750392   1.010587   1.654231
Se     -0.000002   2.021177  16.445769
K_POINTS (automatic)
32      32     1     0 0  0

scf.in

Code: Select all

 &control
    calculation='scf',
    prefix='TaSe2',
    pseudo_dir = '/home/users/nus/e0338235/pseudo/sg15_oncv_upf_2020-02-06',
    outdir='./tmp'
    tstress = .true.,
    tprnfor = .true., 
   etot_conv_thr=1.0D-7
   forc_conv_thr=4.0D-6
/
 &system
    a     =  3.50078e+00
    c     =  1.81000e+01
   ibrav = 4, nat=3, ntyp=2,
    ecutwfc = 80.0
!    ecutrho = 800.0
   occupations='smearing', smearing='fd', degauss=0.005
!   la2f=.true.
/
 &electrons
    mixing_beta = 0.7
    conv_thr =  1.0d-10
 /
ATOMIC_SPECIES
Ta  180.947   Ta_ONCV_PBE-1.2.upf
Se   78.96    Se_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS {angstrom}
Ta       0.000000   0.000000   0.000000
Se      1.750392   1.010587   1.654231
Se     -0.000002   2.021177  16.445769
K_POINTS (automatic)
16      16     1     0 0  0

ph.in

Code: Select all

phonon for NbSe2
 &inputph
  tr2_ph=1.0d-15,
  prefix='TaSe2',
  outdir='./tmp',
  fildvscf='TaSe2pv',
  amass(1)=180.947,
  amass(2)=78.96,
  fildyn='TaSe2.dyn',
  electron_phonon='interpolated',
  el_ph_sigma=0.005,
  el_ph_nsigma=10,
  ldisp=.true.,
!  recover=.true.,  
  nq1=8, nq2=8, nq3=1
 /

EPW input:
scf.in

Code: Select all

 &control
    calculation='scf',
    prefix='TaSe2',
    pseudo_dir = '/home/users/nus/e0338235/pseudo/sg15_oncv_upf_2020-02-06',
    outdir='./tmp'
    tstress = .true.,
    tprnfor = .true., 
   etot_conv_thr=1.0D-7
   forc_conv_thr=4.0D-6
/
 &system
    a     =  3.50078e+00
    c     =  1.81000e+01
   ibrav = 4, nat=3, ntyp=2,
    ecutwfc = 80.0
!    ecutrho = 800.0
   occupations='smearing', smearing='fd', degauss=0.005
/
 &electrons
    mixing_beta = 0.7
    conv_thr =  1.0d-10
 /
ATOMIC_SPECIES
Ta  180.947   Ta_ONCV_PBE-1.2.upf
Se   78.96    Se_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS {angstrom}
Ta       0.000000   0.000000   0.000000
Se      1.750392   1.010587   1.654231
Se     -0.000002   2.021177  16.445769
K_POINTS (automatic)
16      16     1     0 0  0

ph.in

Code: Select all

phonon for TaSe2
 &inputph
  tr2_ph=1.0d-16,
  prefix='TaSe2',
  outdir='./tmp',
  fildvscf='TaSe2pv',
  amass(1)=180.947,
  amass(2)=78.96,
  fildyn='TaSe2.dyn',
  ldisp=.true.,
  nq1=8, nq2=8, nq3=1
 /

nscf.in

Code: Select all

 &control
    calculation='nscf',
    prefix='TaSe2',
    pseudo_dir = '/home/users/nus/e0338235/pseudo/sg15_oncv_upf_2020-02-06',
    outdir='./tmp'
    wf_collect  = .false.
    tstress = .true.,
    tprnfor = .true., 
   etot_conv_thr=1.0D-7
   forc_conv_thr=4.0D-6
/
 &system
    a     =  3.50078e+00
    c     =  1.81000e+01
   ibrav = 4, nat=3, ntyp=2,
    ecutwfc = 80.0
   nbnd = 30
   occupations='smearing', smearing='fd', degauss=0.005
/
 &electrons
    mixing_beta = 0.7
    conv_thr =  1.0d-10
 /
ATOMIC_SPECIES
Ta  180.947   Ta_ONCV_PBE-1.2.upf
Se   78.96    Se_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS {angstrom}
Ta       0.000000   0.000000   0.000000
Se      1.750392   1.010587   1.654231
Se     -0.000002   2.021177  16.445769
K_POINTS crystal
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  0.93750000  0.00000000  0.00000000  3.906250e-03
  0.93750000  0.06250000  0.00000000  3.906250e-03
  0.93750000  0.12500000  0.00000000  3.906250e-03
  0.93750000  0.18750000  0.00000000  3.906250e-03
  0.93750000  0.25000000  0.00000000  3.906250e-03
  0.93750000  0.31250000  0.00000000  3.906250e-03
  0.93750000  0.37500000  0.00000000  3.906250e-03
  0.93750000  0.43750000  0.00000000  3.906250e-03
  0.93750000  0.50000000  0.00000000  3.906250e-03
  0.93750000  0.56250000  0.00000000  3.906250e-03
  0.93750000  0.62500000  0.00000000  3.906250e-03
  0.93750000  0.68750000  0.00000000  3.906250e-03
  0.93750000  0.75000000  0.00000000  3.906250e-03
  0.93750000  0.81250000  0.00000000  3.906250e-03
  0.93750000  0.87500000  0.00000000  3.906250e-03
  0.93750000  0.93750000  0.00000000  3.906250e-03

epw.in

Code: Select all

--
&inputepw
  prefix      = 'TaSe2'
  amass(1)    = 180.947
  amass(2)    = 78.96
  outdir      = './tmp/'

  iverbosity  = 3

  elph        = .true.
  epbwrite    = .true.
  epbread     = .false.

  epwwrite    = .true.
  epwread     = .false.

  nbndsub     =  11
  nbndskip    =  13

  wannierize  = .true.
  num_iter    = 300
  iprint      = 2
  dis_win_max = 6.5
  dis_win_min = -5
  dis_froz_max = 4
  dis_froz_min = -4
  proj(1)     = 'Ta:l=2'   
  proj(2)     = 'Se:l=1'
  wdata(1) = 'bands_plot = .true.'
  wdata(2) = 'begin kpoint_path'
  wdata(3) = 'G 0.00 0.00 0.00 M 0.00 0.50 0.00'
  wdata(4) = 'M 0.00 0.50 0.00 K 0.333 0.333 0.00'
  wdata(5) = 'K 0.333 0.333 0.00 G 0.00 0.00 0.00'
  wdata(6) = 'end kpoint_path'
  wdata(7) = 'bands_num_points = 30'
  wdata(8) = 'dis_num_iter = 10000'
  wdata(9) = 'guiding_centres = .true.'

  elecselfen  = .false.
  phonselfen  = .false.
  a2f         = .false.


  fsthick     = 3 ! eV 
  eptemp      = 30 ! K (same as PRB 76, 165108)
  degaussw    = 0.005 ! eV

  dvscf_dir   = '../../phonon/save'
!  filukk      = './diam.ukk'
!  filqf       = 'meshes/path.dat'
  nkf1        = 160
  nkf2        = 160
  nkf3        = 1
  nqf1        = 80
  nqf2        = 80
  nqf3        = 1

  
  nk1         = 16
  nk2         = 16
  nk3         = 1

  nq1         = 8
  nq2         = 8
  nq3         = 1
 /
      10 cartesian
   0.000000000000000E+00   0.000000000000000E+00   0.000000000000000E+00
   0.000000000000000E+00   0.144337567297387E+00   0.000000000000000E+00
   0.000000000000000E+00   0.288675134594775E+00   0.000000000000000E+00
   0.000000000000000E+00   0.433012701892162E+00   0.000000000000000E+00
   0.000000000000000E+00  -0.577350269189550E+00   0.000000000000000E+00
   0.124999999999992E+00   0.216506350946081E+00   0.000000000000000E+00
   0.124999999999992E+00   0.360843918243469E+00   0.000000000000000E+00
   0.124999999999992E+00   0.505181485540856E+00   0.000000000000000E+00
   0.249999999999985E+00   0.433012701892162E+00   0.000000000000000E+00
   0.249999999999985E+00   0.577350269189550E+00   0.000000000000000E+00

epw-linewidth.in

Code: Select all

--
&inputepw
  prefix      = 'TaSe2'
  amass(1)    = 180.947
  amass(2)    = 78.96
  outdir      = './tmp/'

  iverbosity  = 3

  elph        = .true.
  kmaps       = .true.
  epbwrite    = .false.
  epbread     = .false.

  epwwrite    = .false.
  epwread     = .true.

  nbndsub     =  11
  nbndskip    =  13

  wannierize  = .false.
  num_iter    = 300
  iprint      = 2
  dis_win_max = 6.5
  dis_win_min = -5
  dis_froz_max = 4
  dis_froz_min = -4
  proj(1)     = 'Ta:l=2'   
  proj(2)     = 'Se:l=1'
  wdata(1) = 'bands_plot = .true.'
  wdata(2) = 'begin kpoint_path'
  wdata(3) = 'G 0.00 0.00 0.00 M 0.00 0.50 0.00'
  wdata(4) = 'M 0.00 0.50 0.00 K 0.333 0.333 0.00'
  wdata(5) = 'K 0.333 0.333 0.00 G 0.00 0.00 0.00'
  wdata(6) = 'end kpoint_path'
  wdata(7) = 'bands_num_points = 30'
  wdata(8) = 'dis_num_iter = 10000'
  wdata(9) = 'guiding_centres = .true.'

  elecselfen  = .false.
  phonselfen  = .true.
  a2f         = .false.
  delta_approx= .true.

  fsthick     = 3 ! eV 
  eptemp      = 1 ! K (same as PRB 76, 165108)
  degaussw    = 0.1 ! eV

  dvscf_dir   = '../../phonon/save'
!  filukk      = './diam.ukk'
  filqf       = 'meshes/path.dat'
  nkf1        = 160
  nkf2        = 160
  nkf3        = 1
!  nqf1        = 80
!  nqf2        = 80
!  nqf3        = 1

  
  nk1         = 16
  nk2         = 16
  nk3         = 1

  nq1         = 8
  nq2         = 8
  nq3         = 1
 /
      10 cartesian
   0.000000000000000E+00   0.000000000000000E+00   0.000000000000000E+00
   0.000000000000000E+00   0.144337567297387E+00   0.000000000000000E+00
   0.000000000000000E+00   0.288675134594775E+00   0.000000000000000E+00
   0.000000000000000E+00   0.433012701892162E+00   0.000000000000000E+00
   0.000000000000000E+00  -0.577350269189550E+00   0.000000000000000E+00
   0.124999999999992E+00   0.216506350946081E+00   0.000000000000000E+00
   0.124999999999992E+00   0.360843918243469E+00   0.000000000000000E+00
   0.124999999999992E+00   0.505181485540856E+00   0.000000000000000E+00
   0.249999999999985E+00   0.433012701892162E+00   0.000000000000000E+00
   0.249999999999985E+00   0.577350269189550E+00   0.000000000000000E+00

Thanks in advance if anyone can help the problem.

Sincerely,
Zishen

[zz11ss11zz]

As you may note, the Pb phonon linewidth given by ICTP tutorials from qe and epw are also different except for their different units. (EPW only shows linewidth of third phonon which corresponds to the highest branch in the QE linewidth). I am still confused about the problem...

[hlee]

Dear zz11ss11zz:

Is this a normal phenomenon because EPW has more dense k/q points than QE? I put my input in the following:

I think so; in EPW, you use 160x160x1 dense grids while in ph.x you use 32x32x1 ones.
Additionally, there might be a issue resulting from 2D system, but I don't know much about it; you can check the literature.

Regarding the example in the ICTP school:
I didn't make this tutorial.
Assuming that the q-point path is the same [as you know, in matdyn the q-point path is given in Cart. units while in filqf of epw it is given in Cryst. units (in default)], it seems that the results provided are under converged.
In order to make a meaningful comparison, you should first converge the results and use the same computational parameters, for instance, broadening, etc.

For your info, I would like to point out that ph.x uses the linear interpolation in evaluation of electron-phonon vertex different from EPW. So the convergence behaviour can be different.

Sincerely,

H. Lee

[zz11ss11zz]

Dear H. Lee,

Thank you very much for your reply.

Yes, the q-path is QE and EPW are given in a different way, but we noted that the high symmetry paths are same. And the tutorial indeed said the results are under converged.
I recalculated the example using high accuracy:
For qe: scf0.in 32*32*32 scf.in 16*16*16 ph.in 8*8*8; broadening =0.05
For epw: scf.in 32*32*32 ph.in 8*8*8 nscf.in 16*16*16 (4096 kpoints) epw.in nkf=32*32*32 nqf=8*8*8; degaussw =0.05

The results are similar to the case for TaSe2, the qe linewidth is smooth while the epw linewidth has many peaks. Increasing the nkf/nqf in epw may make the line smooth (this small nkf for comparing), but I think it will also different from qe result.

I cheeked the effects of nkf, nqf, degaussw to the epw linewidth on convergence, I think the convergence has been achieved.
And the TaSe2 qe linewidth seems more in line with expectation...

Sincerely,
Zishen

[hlee]

Dear zz11ss11zz:

Did you take into account the fact that in QE broadening (el_ph_sigma ?) is in Ryd while in EPW broadening (degaussw ?)is in eV?

Sincerely,

H. Lee

[zz11ss11zz]

Dear H. Lee,

Thanks for reminding, I ignored this point.
I recalculated the epw using the correct degaussw=0.68eV (0.05*13.6), the epw results became more close to the qe results. Maybe I should increase nkf/nqf in epw to obtain better results.

Sincerely,
Zishen

[sponce]

Dear Zishen,

Indeed you can try increasing the fine grids (especially the q one) in EPW.

This being said, it seems like the curves are the same/very similar but there is just a factor 2 difference.
You can take a look in EPW/src/selfen.f90 and look for the selfen_phon_q subroutine where the equations used are indicated.
What is computed is the imaginary part of the phonon self-energy which corresponds to the half width (phonon linewidth).

Hope this helps.

Best,
Samuel

[zz11ss11zz]

Dear Professor S. Ponce,

Thank you for your comments.

I tried to increase the nkf, nqf, fsthick and observed the same lead linewidth as before.

Yes, it is a factor 2 difference between qe and epw result. As the imaginary part of phonon self-energy is the half of phonon linewidth, we should expect that the epw result is the half of qe result instead of twice? But the epw phonon linewidth in graph is twice as big as qe linewidth?

I also try to increase the degaussw to correct value in the TaSe2 epw.in, and the result improved. However, I don't understand why epw linewidth equal to zero when x~0.3 and x~1.2. (nkf/nqf has been doubled, the linewidth is same to the original one)

Sincerely,
Zishen

[hlee]

Dear Zishen:

Yes, it is a factor 2 difference between qe and epw result. As the imaginary part of phonon self-energy is the half of phonon linewidth, we should expect that the epw result is the half of qe result instead of twice? But the epw phonon linewidth in graph is twice as big as qe linewidth?

By comparing the expressions for the phonon linewidth (See the subroutine of selfen_phon_q in EPW/src and that of elphsum in PHonon/PH), it is obvious that the phonon linewidth printed in EPW has an additional factor of 2.

(Excerpt from EPW/src/ephwann_shuffle.f90 where the phonon linewidth is printed)

! SP - 03/2019
! \Gamma = 1/\tau = phonon lifetime
! \Gamma = - 2 * Im \Pi^R where \Pi^R is the retarted phonon self-energy.
! Im \Pi^R = pi*k-point weight*[f(E_k+q) - f(E_k)]*delta[E_k+q - E_k - w_q]
! Since gamma_all = pi*k-point weight*[f(E_k) - f(E_k+q)]*delta[E_k+q - E_k - w_q] we have
! \Gamma = 2 * gamma_all

If the imaginary part of phonon self-energy is denoted as gamma_all in both QE and EPW, in QE gamma_all is printed while 2*gamma_all is printed in EPW.
If "Half width at half maximum" (HWHM) is interpreted as the imaginary part of phonon self-energy [J. Noffsinger et al, Comput. Phys. Comm. 181, 2140 (2010)], in EPW "Full width at half maximum" (FWHM) is printed.

Regarding your 2nd question:
I already told you the following:

Additionally, there might be a issue resulting from 2D system, but I don't know much about it; you can check the literature.

Maybe, Samuel can tell you more about it.

Sincerely,

H. Lee

[zz11ss11zz]

Dear H. Lee,

Thank you for your patient explanation.

I note that another thing different from epw and qe:
The prints from EPW/src/ephwann_shuffle.f90 doesn't mention the square of the electron-phonon matrix, and in EPW/src/selfen.f90:

! SP: The expression below is the imag part of phonon self-energy,
! sans matrix elements [Eq. 9 in Comput. Phys. Commun. 209, 116 (2016)]
! = pi * k-point weight * [f(E_k) - f(E_k+q)] * delta[E_k+q - E_k - w_q]

While the print from q-e/PHonon/PH/elphon.f90:

! gamma = \pi \sum_k\sum_{i,j} \delta(e_{k,i}-Ef) \delta(e_{k+q,j}-Ef)
! | \sum_mu z(mu,nu) <psi_{k+q,j}|dvscf_q(mu)*psi_{k,i}> |^2
! where z(mu,nu) is the mu component of normal mode nu (z = dyn)
! gamma(nu) is the phonon linewidth of mode nu

I am not sure whether this different will also affect their results?

I read some paper using epw to study 2d material. I note that one paper (prb 99, 161119 (2019)) mention:

such a calculation of the non-CDW phase lead to the imaginary phonons around qCDW [Fig. S1(b), pink curves], which are frequently excluded in electron-phonon coupling calculation by the mainstream package (such as EPW package used in this work), due to the ill-definition of electron-phonon coupling of imaginary phonons.

And I compare curves between phonon dispersion and linewidth, the epw linewidth equal to zero points is exactly the imaginary phonon dispersion points. I think this is the reason for difference and it may affect other electron-phonon coupling calculations (electron-phonon matrix? electron-phonon constant?).

Sincerely,
Zishen