Trouble with Pade calculations

[since2012]

Dear all,

When I perform a Pade calculations for my system, I found there the calculation closed with a gap closing at a low temperature. In details, the output says following:

Code: Select all

 Finish reading .ephmat files

     a2f file is not found to estimate initial gap: calculating a2f files
 

     Finish reading a2f file

     Electron-phonon coupling strength =    3.5952537
 
     Estimated Allen-Dynes Tc =    61.942534 K for muc =    0.10000
  
     Estimated w_log in Allen-Dynes Tc =    27.593297 meV
  
     Estimated BCS superconducting gap =     9.394518 meV
  
    [b][i] Estimated Tc from machine learning model =   108.283849 K[/i][/b]

Experience speaking, the Estimated Tc from machine learning model should close to the temperature when the pade gap is closed. But for my case, the gap closed at 92 K. Why there is a large difference between them? Ang adivece to fix it?

Best & Regards!
Jianguo Si

[since2012]

Besides, for another system, I met follwing error-end-log:

Code: Select all

Finish reading a2f file

     Electron-phonon coupling strength =    1.3159155
 
     Estimated Allen-Dynes Tc =     9.718795 K for muc =    0.10000
  
     Estimated w_log in Allen-Dynes Tc =     8.400715 meV
  
     Estimated BCS superconducting gap =     1.474002 meV
  
     Estimated Tc from machine learning model =    12.758579 K
  
  
     WARNING WARNING WARNING 
  
     The code may crash since tempsmax =   15.000 K is larger than Allen-Dynes Tc =     9.719 K
    
     temp(  1) =      2.00000 K
    
     Solve anisotropic Eliashberg equations on imaginary-axis
    
     Total number of frequency points nsiw(     1) =    923
     Cutoff frequency wscut =     1.0000
     broyden mixing factor =      0.70000
    
     Actual number of frequency points (     1) =    923 for uniform sampling

     Size of allocated memory per pool: ~=   12.8065 Gb
        iter      ethr          znormi      deltai [meV]
          1   3.316822E+00   2.169270E+00   1.890334E+00
          2   1.917468E-01   2.149809E+00   2.078613E+00
          3   1.651004E-02   2.133386E+00   2.234575E+00
          4   4.926948E-02   2.119017E+00   2.379085E+00
          5   7.551992E-02   2.101841E+00   2.564391E+00
          6   1.227617E-02   2.099744E+00   2.589301E+00
          7   8.060548E-03   2.102010E+00   2.566494E+00
          8   1.930703E-03   2.102636E+00   2.562485E+00
          9   4.748381E-03   2.101706E+00   2.573249E+00
         10   4.823243E-03   2.100781E+00   2.584625E+00
         11   3.462389E-03   2.100153E+00   2.592500E+00
         12   2.320016E-05   2.100139E+00   2.592502E+00
     Convergence was reached in nsiter =     12
 
     Chemical potential (itemp =   1) =    -3.6839000000E+00 eV
 
     Temp (itemp =   1) =    2.000 K  Free energy =    -0.003670 meV
 
     Min. / Max. values of superconducting gap =     0.000000    3.367226 meV
     iaxis_imag   :  27749.17s CPU  27831.28s WALL (       1 calls)
 
    
     Pade approximant of anisotropic Eliashberg equations from imaginary-axis to real-axis
     Cutoff frequency wscut =     1.0000
    
        pade    Re[znorm]   Re[delta] [meV]
        830            NaN            NaN
 
     Convergence was reached for N =    830 Pade approximants
 
     Min. / Max. values of superconducting gap =     0.000000    0.000000 meV

According to some suggestions in EPW forum, i increase npade from 90 to 100, nothing changed but more error informations appeard as

Code: Select all

  
     Pade approximant of anisotropic Eliashberg equations from imaginary-axis to real-axis
     Cutoff frequency wscut =     1.0000
    
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
 One or more Pade coefficients are NaN
        pade    Re[znorm]   Re[delta] [meV]
        924            NaN            NaN
 
     Convergence was reached for N =    924 Pade approximants
 
     Min. / Max. values of superconducting gap =     0.000000    0.000000 meV

How to fix it?

[Shashi]

Hi Jianguo,

To eliminate NaN values, check if the temperature is very close to Tc. If so, try increasing npade to a significantly larger value. If that doesn't resolve the issue, consider increasing the cut-off for the imaginary frequency.

Additionally, the Tc estimated from the machine learning model is obtained differently, and your electron-phonon coupling strength appears quite high. This suggests that the ML-predicted Tc might be overestimated. The gap closing in Pade is closer to the actual value. If you notice anything unusual, try increasing npade and adjusting wscut for Pade calculations.

Let me know if this helps resolve the issue.

Best,
Shashi