## Negative value of superconducting gap

Post here questions linked with issue while running the EPW code

Moderator: stiwari

simba2828
Posts: 45
Joined: Tue Mar 07, 2023 4:19 pm
Affiliation: IIT Kharagpur

### Negative value of superconducting gap

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.

epwwrite = .true.

!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.

!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
Attachments
Screenshot from 2023-03-10 15-24-24.png (5.46 KiB) Viewed 22616 times

hpaudya1
Posts: 191
Joined: Tue Mar 21, 2017 7:11 pm
Affiliation:

### Re: Negative value of superconducting gap

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
Posts: 45
Joined: Tue Mar 07, 2023 4:19 pm
Affiliation: IIT Kharagpur

### Re: Negative value of superconducting gap

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
Posts: 172
Joined: Fri Jan 22, 2016 6:48 pm
Affiliation:

### Re: Negative value of superconducting gap

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
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York

simba2828
Posts: 45
Joined: Tue Mar 07, 2023 4:19 pm
Affiliation: IIT Kharagpur

### Re: Negative value of superconducting gap

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
Posts: 172
Joined: Fri Jan 22, 2016 6:48 pm
Affiliation:

### Re: Negative value of superconducting gap

Hi,

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

Best,
Roxana
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York

simba2828
Posts: 45
Joined: Tue Mar 07, 2023 4:19 pm
Affiliation: IIT Kharagpur

### Re: Negative value of superconducting gap

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
Posts: 20
Joined: Fri Mar 17, 2023 4:28 pm
Affiliation: Binghamton University

### Re: Negative value of superconducting gap

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
Posts: 45
Joined: Tue Mar 07, 2023 4:19 pm
Affiliation: IIT Kharagpur

### Re: Negative value of superconducting gap

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.

epwwrite = .true.

!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.

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
Posts: 31
Joined: Wed Jun 17, 2020 8:55 pm
Affiliation: Binghamton University

### Re: Negative value of superconducting gap

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