Negative value of superconducting gap

[simba2828]

Dear EPW developers and Users,

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:

Code: Select all

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

The followings are the Min/Max values of superconducting gaps with different temps:
temp=8K

Code: Select all

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)

temp = 12K

Code: Select all

 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)

temp = 17K

Code: Select all

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

Code: Select all

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:

Code: Select all

&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
 /

The Wannier projected bands are in good agreement with the DFT band structure. And I selected the values according to a previous post (viewtopic.php?f=3&t=1682) which I also mentioned in the epw input file. The maximum frequency in the phonon dispersion is around 380 cm-1. So accordingly I set fsthick and wscut.

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

[hpaudya1]

Hi Shubham,

The negative value of superconducting gap is not physical. However, we do not restrict the calculation based on the -/+ value of the superconducting gap, any numerical value is possible in the calculation. If the negative value is too small, that can the a numerical error.

I recommend you to do some convergence tests based on your fsthick, fine k/q meshes, and wscut and make sure that the calculation is converged wrt these parameters.

Happy EPWing,
Hari

[simba2828]

Thank You Hari,

Could you please tell me which quantities I check for the convergence for (1) fsthick (2) k/q point and (3) wscut? Say, in scf calculation we can check the ground state energy but what should I check for the above flags? Though I checked several tests with respect to fstick/k/q/wscut but the negative value of SC gap persists.
I checked for (1) k/q 32 32 1/32 32 1 upto 240 240 1 / 120 120 1
(2) fsthick: 2 to 0.4
(3) wscut = 0.4 to 1.0 ! eV 10 times of Upper limit over frequency

What I found that with very fine k/q mesh the lower gap in "prefix.imag_aniso_012.00" file shifts below the 0.0 value. Does it mean that the system does not show a two-gap nature?

Thank you

[roxana]

Hi Shubham,

I would recommend running calculations with different \mu* values starting from \mu*=0 and see at which value the lower gap becomes negative.

Best,
Roxana

[simba2828]

Hello Ma'am,

As you can see that I am using muc=0.05, which is already very close to zero. Still I will check with zero and close to zero values and check what you suggest. Though I checked with higher values of muc but the problem persists.

Thank you
Shubham

[roxana]

Hi,

Larger the \mu* value stronger the Coulomb effect and therefore smaller the Tc and gap.

Best,
Roxana

[simba2828]

Hello Ma'am,

I checked again my calculations with zero and lower mu*. With zero mu, the "Min Superconducting gap" is also zero but even a small mu value (0.01) the "Min Superconducting gap" becomes negative. Would you like to comment on that please?

Thank you

[hmori]

Hi Shubham,

For your calculations using muc=0.0 and 0.01, what values did you use for parameters such as wscut? Did the "Max Superconducting gap" remain positive when the "Min Superconducting gap" was negative?

Best,
Hitoshi

[simba2828]

Hello Sir,

I am using wscut = 0.4 eV which is 10 times of Upper limit over frequency integration. And yes, the "Max Superconducting gap" remain positive when the "Min Superconducting gap" was negative. I am attaching my input again for your consideration.

Code: Select all

--
&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= 4.6
  dis_froz_min= -5.8

  !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     = 0.15 ! meV
  nqstep       = 500

  eliashberg  = .true.

  laniso = .true.
  limag = .true.
  lpade = .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)  = 32
  temps(2)  = 17
  temps(3)  = 34
  temps(4) = 27
  temps(5) = 35.5
  temps(6) = 36

  !max_memlt = 5  !GB
  !vme=.false. 

  nsiter   = 500
  degaussw    = 0.04 ! eV ~  1/4 of fsthick
  wscut = 0.4   ! eV 10 times of  Upper limit over frequency integration/summation in the Elisashberg eq(1 cm-1 ~ 1/8000 eV)
  fsthick     = 0.5  ! eV ~ 4 times the maximum phonon frequency 
  muc     = 0.01

  dvscf_dir   = '../ph6/save'
  
  !system_2d = .true.

  nk1         = 16
  nk2         = 16
  nk3         = 1

  nq1         = 4
  nq2         = 4
  nq3         = 1

  mp_mesh_k = .true.
  nkf1 = 120
  nkf2 = 120
  nkf3 = 1

  nqf1 = 60
  nqf2 = 60
  nqf3 = 1
 /

Kindly let me know if anything else I can provide. I'd appreciate the help.

Thank you

[gkafle1]

Hi simba2828,

Can you please check first if your Wannierization is good to go for further calculations? You can check the fitting of the Wannier bands with the DFT bands, the symmetry of the Wannier functions, the Wannier function spreads, and the decay of the matrix elements in real space.

Thanks!

Gyanu