After successfully finishing the phonon, scf and nscf calculations I am trying to calculate superconducting properties for my 2D system.

I notice that the Min. value of superconducting Gap is negative after all the cycles with different temperatures (8K, 12K, 17K and 20K I tried) with Estimated Tc = 14.91 K. The following is from my epw.out file:

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```
Estimated Allen-Dynes Tc = 14.910578 K for muc = 0.05000
Estimated w_log in Allen-Dynes Tc = 12.156787 meV
Estimated BCS superconducting gap = 2.261414 meV
Estimated Tc from machine learning model = 17.992366 K
WARNING WARNING WARNING
The code may crash since tempsmax = 20.000 K is larger than Allen-Dynes Tc = 14.911 K
temp( 1) = 8.00000 K
Solve anisotropic Eliashberg equations on imaginary-axis
Total number of frequency points nsiw( 1) = 23
Cutoff frequency wscut = 0.1018
```

temp=8K

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```
Convergence was reached in nsiter = 25
Chemical potential (itemp = 1) = -1.8116930967E+00 eV
Temp (itemp = 1) = 8.000 K Free energy = -0.009477 meV
Min. / Max. values of superconducting gap = [color=#FF0000] -0.340667[/color] 4.740647 meV
iaxis_imag : 10.70s CPU 10.78s WALL ( 1 calls)
Pade approximant of anisotropic Eliashberg equations from imaginary-axis to real-axis
Cutoff frequency wscut = 0.1000
pade Re[znorm] Re[delta] [meV]
20 1.999132E+00 3.304228E+00
Convergence was reached for N = 20 Pade approximants
Min. / Max. values of superconducting gap =[color=#FF0000] -0.353636 [/color] 5.027398 meV
raxis_pade : 1.13s CPU 3.37s WALL ( 1 calls)
```

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```
Convergence was reached in nsiter = 15
Chemical potential (itemp = 2) = -1.8116930967E+00 eV
Temp (itemp = 2) = 12.000 K Free energy = -0.006623 meV
Min. / Max. values of superconducting gap = [color=#FF0000] -0.335653 [/color] 4.569238 meV
iaxis_imag : 13.65s CPU 13.76s WALL ( 2 calls)
Pade approximant of anisotropic Eliashberg equations from imaginary-axis to real-axis
Cutoff frequency wscut = 0.1000
pade Re[znorm] Re[delta] [meV]
14 2.068469E+00 3.184121E+00
Convergence was reached for N = 14 Pade approximants
Min. / Max. values of superconducting gap = [color=#FF0000] -0.333999[/color] 4.926744 meV
raxis_pade : 2.31s CPU 6.50s WALL ( 2 calls)
```

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```
Convergence was reached in nsiter = 29
Chemical potential (itemp = 3) = -1.8116930967E+00 eV
Temp (itemp = 3) = 17.000 K Free energy = -0.002380 meV
Min. / Max. values of superconducting gap = [color=#FF0000]-0.290275 [/color] 3.723432 meV
iaxis_imag : 16.98s CPU 17.13s WALL ( 3 calls)
Pade approximant of anisotropic Eliashberg equations from imaginary-axis to real-axis
Cutoff frequency wscut = 0.1000
pade Re[znorm] Re[delta] [meV]
10 2.152384E+00 2.402631E+00
Convergence was reached for N = 10 Pade approximants
Min. / Max. values of superconducting gap = [color=#FF0000] -0.332317 [/color] 5.359331 meV
raxis_pade : 3.47s CPU 9.73s WALL ( 3 calls)
```

temp = 20K

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```
Convergence was reached in nsiter = 47
Chemical potential (itemp = 4) = -1.8116930967E+00 eV
Temp (itemp = 4) = 20.000 K Free energy = -0.000623 meV
Min. / Max. values of superconducting gap = [color=#FF0000]-0.224141[/color] 2.739538 meV
iaxis_imag : 20.75s CPU 20.94s WALL ( 4 calls)
Pade approximant of anisotropic Eliashberg equations from imaginary-axis to real-axis
Cutoff frequency wscut = 0.1000
pade Re[znorm] Re[delta] [meV]
8 2.308737E+00 1.123975E+00
Convergence was reached for N = 8 Pade approximants
Min. / Max. values of superconducting gap = [color=#FF0000]0.224891[/color] 3.098743 meV
```

The following is my epw input file:

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```
&inputepw
prefix = 'nsms',
outdir = './out/'
ep_coupling = .true.
elph = .true.
epbwrite = .true.
epbread = .false.
epwwrite = .true.
epwread = .false.
!etf_mem = 1
nbndsub = 17,
!nbndskip = 0
bands_skipped = 'exclude_bands = 1:12,30,31'
wannierize = .false.
num_iter = 500
dis_froz_max= 0.9
dis_froz_min= -7.5
!wdata(1) = 'exclude_bands=30,31'
wdata(1) = 'dis_mix_ratio = 0.5'
wdata(2) = 'dis_num_iter = 2000'
wdata(3) = 'bands_plot : true'
wdata(4) = 'bands_num_points : 300'
wdata(5) = 'bands_plot_format : xmgrace gnuplot'
wdata(6) = 'begin kpoint_path'
wdata(7) = 'M 0.5 0.0 0.0 K 0.3333 0.3333 0.0'
wdata(8) = 'K 0.3333 0.3333 0.0 G 0.0 0.0 0.0'
wdata(9) = 'G 0.0 0.0 0.0 M 0.5 0.0 0.0'
wdata(10) = 'end kpoint_path'
iverbosity = 2
eps_acustic = 0.1 ! Lowest boundary for the phonon frequency
ephwrite = .true. ! Writes .ephmat files used when Eliasberg = .true.
nsmear = 1
delta_smear = 0.01 ! eV 0.04
degaussq = 0.5 ! meV
nqstep = 500
eliashberg = .true.
laniso = .true.
limag = .true.
lpade = .true.
!lifc = .true.
fermi_plot = .true.
conv_thr_iaxis = 1.0d-4
!nstemp = 1 ! Nr. of temps
!temps = 15.00 ! K provide list of temperetures OR (nstemp and temps = tempsmin tempsmax for even space mode)
temps(1) = 8
temps(2) = 12
temps(3) = 17
temps(4) = 20
!temps(5) = 6
!max_memlt = 5 !GB
!vme=.false.
nsiter = 500
[color=#FF0000]degaussw = 0.04 ! eV ~ 1/4 of fsthick
wscut = 0.5 ! eV 10 times of Upper limit over frequency integration/summation in the Elisashberg eq(1 cm-1 ~ 1/8000 eV)
fsthick = 0.18 ! eV ~ 4 times the maximum phonon frequency
muc = 0.05[/color]
dvscf_dir = '../phonon_angs/save'
!system_2d = .true.
nk1 = 20
nk2 = 20
nk3 = 1
nq1 = 4
nq2 = 4
nq3 = 1
mp_mesh_k = .true.
nkf1 = 60
nkf2 = 60
nkf3 = 1
nqf1 = 60
nqf2 = 60
nqf3 = 1
/
```

Also When I plot Superconducting gap along the imaginary axis from the file "nsms.imag aniso 008.00", I see that the gap value goes in the negative region. I am attaching the figure here.

Could someone please help me out why I am getting the negative Min. superconducting gap and this negative region delta?

Sincerely,

Shubham

IIT Kharagpur, India