EPW's lambda is inconsistent with QE's result

[qiaoqiao66]

Dear Experts and users,
In our calculation, we have taken the smaller k and q mesh to compute the lambda in the QE calculation, due to the calculation system is complex. In order to get more accurate calculation results, we choose the EPW for further calculation.
How to ensure the reasonable calculation result of epw, here's what we think. In the case that wannierized band and phonon structure agree well with those calculated by QE, in our EPW calculations, if the fine k mesh nkf(1-3)= the k mesh in scf.a2f.in, and the fine q mesh nqf(1-3) = the nq(1-3) in ph.in, and the degaussw = degauss in lambda.out, then the results should be consistent with those calculated by QE. But we didn't get consistent results. So I would like to ask the experts and users:

1. In superconducting property calculations, when QE calculation and EPW calculation use the same parameters (set the fine k mesh nkf(1-3)= the k mesh in scf.a2f.in, and the fine q mesh nqf(1-3) = the nq(1-3) in ph.in, and the degaussw = degauss in lambda.out), is the calculated Election-phonon coupling ‘lambda’ exactly the same?

2. Is the meaning of degaussw (eV) in EPW calculation consistent with that of degauss (Ry) in lambda.out ?

Have you ever had the same problem or if you know what caused it, would you please let me know?
Thanks a lot!!!
Best regards,
Zhi Yuan

[hlee]

Dear Zhi Yuan:

Could you provide with us the relevant information such as (1) the plots which can show us how different EPW's lambda is from QE's one and (2) (at least) all inputs of QE and EPW calculations?

Sincerely,

H. Lee

[qiaoqiao66]

Dear H. Lee，

Thank you very much for your feedback H. Lee. Recently I tested the MgB2 example again and encountered the same problem. I attached the input and output of the calculation in the attachment.

The main results are listed here.

Just to compare it with what we did with QE, we tested lambda values at different degaussw.

mg.degaussw.0.068.out0 means, in the calculation, the degaussw is 0.068.

The data listed under lambda.out represents the lambda values under different degauss output from
the lambd.out file calculated by QE (here the unit of degauss is the same as the unit of degaussw(eV)

QE: scf 888 scf.fit 323232 ph 444 EPW: scf 888 nscf 888 nkf(1-3) = 32 nqf(1-3) = 4
lambda.out
mg.degaussw.0.068.out0: Electron-phonon coupling strength = 0.8695396 0.84153
mg.degaussw.0.136.out0: Electron-phonon coupling strength = 0.7378657 0.69551
mg.degaussw.0.204.out0: Electron-phonon coupling strength = 0.6918787 0.66267
mg.degaussw.0.272.out0: Electron-phonon coupling strength = 0.6545563 0.63236
mg.degaussw.0.34 .out0: Electron-phonon coupling strength = 0.6204697 0.60483
mg.degaussw.0.408.out0: Electron-phonon coupling strength = 0.5901535 0.58002


QE:scf 888 scf.fit 323232 ph 444 EPW: scf 888 nscf 888 nkf(1-3) = 16 nqf(1-3) = 4
lambda.out
mg.degaussw.0.068.out0: Electron-phonon coupling strength = 0.8368109 0.71562
mg.degaussw.0.136.out0: Electron-phonon coupling strength = 0.7216039 0.69338
mg.degaussw.0.204.out0: Electron-phonon coupling strength = 0.6583039 0.66430
mg.degaussw.0.272.out0: Electron-phonon coupling strength = 0.6164626 0.63021
mg.degaussw.0.34.out0: Electron-phonon coupling strength = 0.5936238 0.60236
mg.degaussw.0.408.out0: Electron-phonon coupling strength = 0.5756075 0.57940

Sincerely,

Zhi Yuan

[hlee]

Dear Zhi Yuan:

In the phonon code of QE, lambda is calculated by using the "double-delta function approximation"; see the equations (2), (3), and (5) in the "A Appendix: Electron-phonon coefficients" of the page at https://www.quantum-espresso.org/Doc/ph_user_guide.pdf .

In EPW, unless if you use delta_approx = .true. ( https://docs.epw-code.org/doc/Inputs.html#delta-approx ), you start from the Eq. (1) of J. Noffsinger et al., Comput. Phys. Comm. 181, 2140 (2010) at https://www.sciencedirect.com/science/a ... via%3Dihub .

Therefore, rigorously speaking, you are using the different expressions.
Please see the section of 3.1. Physical quantities (selfen_phon, selfen_elec, a2f) in the above paper.
Also please check the related previous posts at viewtopic.php?f=3&t=1294 .

Regarding degaussw (eV unit) in EPW and el_ph_sigma (Ryd unit) in the phonon code of QE, both of them are used to mimic the Dirac delta function.

Sincerely,

H. Lee

[qiaoqiao66]

Dear H. Lee,
Thanks a lot for your reply. After following your advice,I use the delta_approx = .true. in epw calculation, the results and input are listed following: (1) the degaussw (eV unit) in EPW and el_ph_sigma (Ryd unit) in the phonon code of QE, we've done the unit conversion in our calculation.
(2) We took the denser degauss and tested it, and found that the smaller degaussw, the greater the difference.

degaussw(eV) lambda epw-double
0.0136 2.33105 2.0380290
0.0272 1.47561 1.2926744
0.0340 1.13700 1.1739702
0.0408 0.94841 1.0913020
0.0544 0.84151 0.9561283
0.068 0.77790 0.8635238
0.0816 0.74014 0.8077838
0.1088 0.71808 0.7577952
0.1224 0.70464 0.7456114
0.136 0.69550 0.7354611
0.204 0.66267 0.6910315
0.272 0.63236 0.6543166
0.34 0.60483 0.6203189
0.408 0.58002 0.5900101

--
&inputepw
prefix = 'MgB2',
amass(1) = 24.305,
amass(2) = 10.811
outdir = './'

ep_coupling = .true.
elph = .true.
kmaps = .true.
epbwrite = .false.
epbread = .false.
epwwrite = .false.
epwread = .true.

nbndsub = 5,
nbndskip = 0

wannierize = .false.
num_iter = 500
dis_froz_max= 8.8
proj(1) = 'B:pz'
proj(2) = 'f=0.5,1.0,0.5:s'
proj(3) = 'f=0.0,0.5,0.5:s'
proj(4) = 'f=0.5,0.5,0.5:s'

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

eps_acustic = 5.0 ! Lowest boundary for the
ephwrite = .true. ! Writes .ephmat files used when wliasberg = .true.

fsthick = 2 ! eV
eptemp = 300 ! K
degaussw = 0.0136 ! eV
degaussq = 0.5 ! meV
nqstep = 500

delta_smear = 0.01 ! eV

wscut = 0.5 ! eV Upper limit over frequency integration/summation in the Elisashberg eq

muc = 0.1

dvscf_dir = './save'

nk1 = 8
nk2 = 8
nk3 = 8

nq1 = 4
nq2 = 4
nq3 = 4

nkf1 = 32
nkf2 = 32
nkf3 = 32

nqf1 = 4
nqf2 = 4
nqf3 = 4
/
12 cartesian
0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00
0.000000000000000E+00 0.000000000000000E+00 0.218900880431704E+00
0.000000000000000E+00 0.000000000000000E+00 -0.437801760863408E+00
0.000000000000000E+00 0.288675134594802E+00 0.000000000000000E+00
0.000000000000000E+00 0.288675134594802E+00 0.218900880431704E+00
0.000000000000000E+00 0.288675134594802E+00 -0.437801760863408E+00
0.000000000000000E+00 -0.577350269189605E+00 0.000000000000000E+00
0.000000000000000E+00 -0.577350269189605E+00 0.218900880431704E+00
0.000000000000000E+00 -0.577350269189605E+00 -0.437801760863408E+00
0.250000000000009E+00 0.433012701892204E+00 0.000000000000000E+00
0.250000000000009E+00 0.433012701892204E+00 0.218900880431704E+00
0.250000000000009E+00 0.433012701892204E+00 -0.437801760863408E+00

Sincerely,
Zhi Yuan

[qiaoqiao66]

Dear H. Lee,
I'm sorry to bother you again. Thank you for your previous patient explanation. I'd like to ask you a few more questions.
(1) According to the "School 2018-Hands-on Session (Wed.4)", to check how each quantity is decaying within the supercell corresponding to our initial k and q grids, we can plot the files decay.H (Hamiltonian), decay.D (dynamical matrix) and decay.epmat_wanep. But in our calculation, the file decay.dynmat or decay.D are not found. On examination we found because we have put the lphase = .true. in the epw.in. I would like to ask you if in this case, do we have any other files that we can use to determine whether the initial Q value is sufficient? Or can only be recalculated without lphase = .true. in the epw.in?
(2) I would like to ask you how to ensure the reasonable calculation result of epw? According to our current understanding, first, we should compare the band structure and phonon dispersion with the results from QE.
Second, according to the decay.H, decay.D and decay.epmat_wanep to check the quantity of our initial k and q grids. Third we have done the comparison of QE and epw with the same computational parameters, But we didn't get consistent results (which are presented in above mail). Does the comparison meaningful?

According to your advice, we have learned the related previous posts at viewtopic.php?f=3&t=1294 . We find two reasons: ph.x uses the linear interpolation in evaluation of electron-phonon vertex different from EPW, So the convergence behaviour can be different; the phonon linewidth printed in EPW has an additional factor of 2. Should the inconsistencies in our calculations also come from these two points?

I am looking forward to receiving your reply. Thank you very much!

Sincerely,
Zhi Yuan