EPW Forum

Hello everyone,

I'm trying to compute the superconducting critical temperature (Tc) for a material using EPW, but I’m encountering an issue with the electron-phonon coupling constant (λ) being much larger than expected.

In the original publication, λ is reported to be around 0.2, with Tc > 65 K. However, my calculations are yielding anomalously large values of λ — far from the reported range.

Here’s what I’ve tried so far:

Wannierization accuracy:
Initially, I suspected a poor Wannierization. I have tested both manual projections and the SCDM method, but the coupling constant remains unusually high.

q-grid density:
I now suspect the sparse q-point mesh might be the source of the error, but I'm not entirely sure how critical that is or if there are other contributing factors I'm missing.

Attached:
Input files for both ph.x and epw.x

Has anyone encountered similar discrepancies?
What’s the best way to confirm whether it’s a q-grid issue, interpolation artifact, or something else (e.g., ep_coupling cutoff, smearing, etc.)?

Any insights or suggestions are most welcome!

Thanks in advance.


&inputph
prefix = 'Mg2IrH6',
fildyn = 'Mg2IrH6.dyn',
amass(1) = 24.305, ! Mg mass
amass(2) = 1.00794, ! H mass
amass(3) = 192.217, ! Ir mass
outdir = './',
ldisp = .true.,
trans = .true.,
fildvscf = 'dvscf',
fildrho = 'drho',
nq1 = 4,
nq2 = 4,
nq3 = 4,
nk1 = 18,
nk2 = 18,
nk3 = 18,
tr2_ph = 1.0d-16,
!alpha_mix(1) = 0.5\,
verbosity = 'high'
/

'--
&inputepw
prefix = 'Mg2IrH6',
outdir = './'

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

epwwrite = .true.
epwread = .false.

etf_mem = 1


nbndsub = 23,

wannierize = .true.
num_iter = 100

scdm_proj = .true.
scdm_entanglement = 'erfc'
auto_projections = .true.
scdm_mu = 6.59389 !-4.948
scdm_sigma = 2.62317 !6.804

iverbosity = 2

!eps_acustic = 1.0 ! Lowest boundary for the phonon frequency
ephwrite = .true. ! Writes .ephmat files used when Eliasberg = .true.

fsthick = 0.1 ! eV
degaussw = 0.01 ! eV
nsmear = 1
delta_smear = 0.04 ! eV

degaussq = 0.5 ! meV
nqstep = 500


eliashberg = .true.

laniso = .true.
limag = .true.
lpade = .true.

conv_thr_iaxis = 1.0d-4

wscut = 1.0 ! eV Upper limit over frequency integration/summation in the Elisashberg eq

nstemp = 1 ! Nr. of temps $
temps = 20 ! K provide list of temperetures OR (nstemp and temps = tempsmin tempsmax for even space mode) $

nsiter = 500

muc = 0.1

dvscf_dir = '../phonons/save'

nk1 = 12
nk2 = 12
nk3 = 12

nq1 = 4
nq2 = 4
nq3 = 4

mp_mesh_k = .true.
nkf1 = 36
nkf2 = 36
nkf3 = 36

nqf1 = 12
nqf2 = 12
nqf3 = 12
/

Dear Mab,

I have a few points I would like to clarify regarding your setup:

Have you compared the phonon results using a 4×4×4 q-grid with those reported in the literature?

The current 12×12×12 q-grid appears to be quite coarse. I recommend increasing the q-grid density, as too small a grid can sometimes lead to unconverged results and an overestimated electron-phonon coupling constant. Please perform a convergence test to verify this.

Additionally, please check whether a fsthick value of 0.1 eV is sufficient for your system. You might also consider increasing the degaussw parameter to see if it improves the results.

If you can share your input and output test files, I would be happy to take a closer look and offer more specific suggestions.

Best regards,
Shashi

Dear Shashi,

Thank you for your reply.

Yes, I have compared the phonon results using 4x4x4 q-grid.

I have also compared the results for 12x12x12 and 36x36x36 nqf grids. There is no difference in results as you can see below:

For 36x36x36 nqf grid:

Electron-phonon coupling strength = 1.4468534

Estimated Allen-Dynes Tc = 69.241513 K for muc = 0.10000

Estimated w_log in Allen-Dynes Tc = 54.202859 meV

Estimated BCS superconducting gap = 10.501519 meV

Estimated Tc from machine learning model = 91.665387 K


For 12x12x12 nqf grid:

Electron-phonon coupling strength = 1.4468534

Estimated Allen-Dynes Tc = 69.241513 K for muc = 0.10000

Estimated w_log in Allen-Dynes Tc = 54.202859 meV

Estimated BCS superconducting gap = 10.501519 meV

Estimated Tc from machine learning model = 91.665387 K

Further, my system consists on just one band that crosses the fermi level back and forth quite a few times. How can I select fsthick in such a case?
What could be the values of degaussw that I can use?

Here is my input file:
'--
&inputepw
prefix = 'Mg2IrH6',
outdir = './'

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

epwwrite = .true.
epwread = .false.

etf_mem = 1

nbndsub = 23,

wannierize = .true.
num_iter = 100

scdm_proj = .true.
scdm_entanglement = 'erfc'
auto_projections = .true.
scdm_mu = 6.59389 !-4.948
scdm_sigma = 2.62317 !6.804

iverbosity = 2

!eps_acustic = 1.0 ! Lowest boundary for the phonon frequency
ephwrite = .true. ! Writes .ephmat files used when Eliasberg = .true.

fsthick = 0.1 ! eV
degaussw = 0.01 ! eV
nsmear = 1
delta_smear = 0.04 ! eV

degaussq = 0.5 ! meV
nqstep = 500


eliashberg = .true.

laniso = .true.
limag = .true.
lpade = .true.

conv_thr_iaxis = 1.0d-4

wscut = 1.0 ! eV Upper limit over frequency integration/summation in the Elisashberg eq

nstemp = 1 ! Nr. of temps $
temps = 20 ! K provide list of temperetures OR (nstemp and temps = tempsmin tempsmax for even space mode) $

nsiter = 500

muc = 0.1

dvscf_dir = '../phonons/save'

nk1 = 12
nk2 = 12
nk3 = 12

nq1 = 4
nq2 = 4
nq3 = 4

mp_mesh_k = .true.
nkf1 = 36
nkf2 = 36
nkf3 = 36

nqf1 = 36
nqf2 = 36
nqf3 = 36
/

Dear Mab,

Thanks for sharing the q-grid results. If you find good convergence with q-grid sizes but still suspect the results are incorrect, I suggest checking your Wannierization. In particular, make sure the orbital spreads are small and well converged with respect to iterations. Otherwise, please share your .wout file.

Regarding your fsthick window convergence, I recommend testing whether varying the fsthick window from 0.1 to 0.2 or 0.4 eV changes the results significantly. This will give you a better sense of fsthick convergence. For these tests, I would also suggest switching off aniso using laniso = .false. and then comparing the lambda values and the a2f file.

Generally, we consider degaussw ~ fsthick/4 or slightly smaller. You can also test for your system by fixing fsthick, then varying degaussw, and comparing the results.

If you would like more specific suggestions, please share your input and output files.

Regards,
Shashi

Dear Shashi,

Thanks for the quick reply again.

I have used the SCDM method for wannierization with mu and sigma estimated based on projectability vs energy plot. Here are the results from the xmgrace non linear curve fitting method based on the function: y = 0.5 * erfc( ( x - A0 ) / A1 )

chi-square: 216.94
correlation coefficient: 0.880928
RMS relative error: 1.37126
Theil U coefficient: 0.0741709

Also, below is the list of spreads from the .wout file corresponding to the epw.out file:
Final State
WF centre and spread 1 ( 1.297767, 0.926548, 2.528593 ) 0.30719912
WF centre and spread 2 ( -1.299197, -0.919858, -2.527823 ) 0.12848678
WF centre and spread 3 ( -1.380000, -0.819852, -2.190190 ) 0.13144682
WF centre and spread 4 ( 1.374666, 0.832415, 2.195558 ) 0.36791959
WF centre and spread 5 ( -1.260674, -1.050413, -2.279565 ) 0.15392374
WF centre and spread 6 ( 1.258546, 1.054382, 2.278883 ) 0.22396930
WF centre and spread 7 ( -1.448061, -1.019883, -2.334561 ) 0.15996019
WF centre and spread 8 ( 1.448805, 1.020595, 2.334778 ) 0.16299073
WF centre and spread 9 ( 2.923126, 2.092294, 0.003466 ) 2.56452998
WF centre and spread 10 ( -1.468349, 2.094367, -2.525151 ) 2.29973961
WF centre and spread 11 ( 1.212790, -1.677010, -2.142680 ) 3.22316824
WF centre and spread 12 ( 0.929739, -1.450852, 1.952322 ) 1.47434960
WF centre and spread 13 ( -2.191455, -1.471834, 0.142806 ) 1.40848104
WF centre and spread 14 ( 2.622894, 1.797846, 4.474411 ) 1.76230616
WF centre and spread 15 ( -2.527886, -1.726115, -0.346114 ) 1.64588747
WF centre and spread 16 ( -1.118071, 1.781066, 2.256553 ) 2.05680563
WF centre and spread 17 ( -1.353469, 1.758002, -2.343518 ) 1.53081903
WF centre and spread 18 ( 0.580927, -0.945631, -1.143952 ) 3.29098489
WF centre and spread 19 ( -0.677652, 1.008125, -1.220549 ) 2.31459910
WF centre and spread 20 ( 1.355282, 0.944794, -0.001490 ) 2.29803160
WF centre and spread 21 ( -0.695416, 0.880959, 1.149806 ) 3.61842451
WF centre and spread 22 ( 1.310174, 1.260460, 2.124810 ) 12.95546664
WF centre and spread 23 ( 1.156778, 1.756741, 3.100659 ) 15.10357075
Sum of centres and spreads ( 2.051264, 8.127143, 5.487053 ) 59.18306050

Spreads (Ang^2) Omega I = 33.677174099
================ Omega D = 4.034018755
Omega OD = 21.471884150
Final Spread (Ang^2) Omega Total = 59.183077004

Currently I am performing the convergence test regarding fsthick and degaussw. I will share the results soon. Please let me know the issues with the above information.

Regards,
Mab

Dear Mab,

Wannier function spread of 12 and 15 Ang, seems to be very large. Please try to reduce the spread of the following orbitals

WF centre and spread 22 ( 1.310174, 1.260460, 2.124810 ) 12.95546664
WF centre and spread 23 ( 1.156778, 1.756741, 3.100659 ) 15.10357075


Regards,
Shashi

Dear Shashi,

The bands 22 and 23 are above the fermi level and this is the best spread I am getting by fitting erfc according to the scdm method. So, I have removed the bands. However, there is no significant effect on the results.

Further, I have also tried to improve the results by changing fsthick from 0.1 to 0.2 and then to 0.4 as you suggested earlier. Here are the results along with the input files:

input-1:
nbndsub = 21,

wannierize = .true.
num_iter = 100

scdm_proj = .true.
scdm_entanglement = 'erfc'
auto_projections = .true.
scdm_mu = 6.59389 !-4.948
scdm_sigma = 2.62317 !6.804

iverbosity = 2

!eps_acustic = 1.0 ! Lowest boundary for the phonon frequency
ephwrite = .true. ! Writes .ephmat files used when Eliasberg = .true.

fsthick = 0.2 ! eV
degaussw = 0.01 ! eV
nsmear = 1
delta_smear = 0.04 ! eV

degaussq = 0.5 ! meV
nqstep = 500


eliashberg = .true.

laniso = .false.
limag = .true.
lpade = .true.

output-1:
Electron-phonon coupling strength = 0.3727781

Estimated Allen-Dynes Tc = 2.056654 K for muc = 0.10000

Estimated w_log in Allen-Dynes Tc = 64.741835 meV

Estimated BCS superconducting gap = 0.311923 meV

Estimated Tc from machine learning model = 1.712806 K

input-2:
nbndsub = 25,

wannierize = .true.
num_iter = 100

scdm_proj = .true.
scdm_entanglement = 'erfc'
auto_projections = .true.
scdm_mu = 6.59389 !-4.948
scdm_sigma = 2.62317 !6.804

iverbosity = 2

!eps_acustic = 1.0 ! Lowest boundary for the phonon frequency
ephwrite = .true. ! Writes .ephmat files used when Eliasberg = .true.

fsthick = 0.2 ! eV
degaussw = 0.01 ! eV
nsmear = 1
delta_smear = 0.04 ! eV

degaussq = 0.5 ! meV
nqstep = 500


eliashberg = .true.

laniso = .false.
limag = .true.
lpade = .true.

output-2:
Electron-phonon coupling strength = 0.3727781

Estimated Allen-Dynes Tc = 2.056654 K for muc = 0.10000

Estimated w_log in Allen-Dynes Tc = 64.741835 meV

Estimated BCS superconducting gap = 0.311923 meV

Estimated Tc from machine learning model = 1.712806 K

input-3:
nbndsub = 23,

wannierize = .true.
num_iter = 100

scdm_proj = .true.
scdm_entanglement = 'erfc'
auto_projections = .true.
scdm_mu = 6.59389 !-4.948
scdm_sigma = 2.62317 !6.804

iverbosity = 2

!eps_acustic = 1.0 ! Lowest boundary for the phonon frequency
ephwrite = .true. ! Writes .ephmat files used when Eliasberg = .true.

fsthick = 0.4 ! eV
degaussw = 0.01 ! eV
nsmear = 1
delta_smear = 0.04 ! eV

degaussq = 0.5 ! meV
nqstep = 500


eliashberg = .true.

laniso = .true.
limag = .true.
lpade = .true.

output-3:
Electron-phonon coupling strength = 0.3727781

Estimated Allen-Dynes Tc = 2.056654 K for muc = 0.10000

Estimated w_log in Allen-Dynes Tc = 64.741835 meV

Estimated BCS superconducting gap = 0.311923 meV

Estimated Tc from machine learning model = 1.712806 K


I have varied the nbndsub and fsthick parameters. The EPC constant is reduced but the Tc shows a significant reduction. Please have a look at it.

Regards,
Mab

Dear Mab,

The electron coupling constant of about 0.3 and a large w_log (65 meV) indeed lead to a small Tc according to the Allen-Dynes expression.
However, as I understand from your input file, you would like to calculate the Tc using the anisotropic Eliashberg equations, right?
In this formalism, your Tc can come out very different from the Allen-Dynes estimate. You only need to run the calculation for a couple of temperatures in some range and see for which temperature the gap reduces to 0.
For additional details, input files and plotting scripts, you can take a look at the EPW school documents: https://docs.epw-code.org/doc/School2024.html.

Note that also for MgB2, the Allen-Dynes estimate gives a Tc of about 7K, but the anisotropic formalism gives a much larger value (~50K), so I believe these estimated values shouldn't be a problem.

Good luck!

Nina.

Dear Mab,

From the results you shared, changing fsthick does not appear to affect the EPC or Tc values. However, you mentioned that the EPC constant is reduced while Tc shows a significant drop. Could you please clarify this?

Second, it seems you have not varied the degaussw values when adjusting fsthick. In many cases, setting degaussw = fsthick / 4 works well. If degaussw (the electronic state smearing) remains fixed, the results may not show much variation. Could you try using degaussw = fsthick / 4 and recheck?

Third, I suggest testing with larger k-grids, at least 48×48×48. In some systems, even a 36×36×36 grid may be insufficient, especially if there is a large variation in DOS near the Fermi energy (e.g., near a van Hove singularity).

If you need further clarification, please feel free to share your input files.

Regards,
Shashi

Dear Nina and Shashi,

Thanks again for your replies,

You can see that when my fsthick was 0.1 eV (earlier posts in the same thread), the Tc was higher (more than 60K) but when my fsthick was increased to 0.2 eV or more, the Tc dropped to around 2K. I am not at all sure what is this supposed to mean? I know that this is some kind of convergence issue. But how can it be resolved?

Regards,
Abhijeet