Interpreting the results of the monolayer MgB2

[CHILLL]

Dear expert and users,

Recently, I calculated superconducting properties of the monolayer MgB2 in EPW. The results weren't good, so I started to look for a possible solution. Wannierization looked good, and from the DFT side I couldn't find any problems.
I have found out that 2D materials should be treated with some k-points in the z direction, and I tried that to see if it will turn the things around. The results didn't change, I still have the same problems as I had with no k-points in the z direction.

The results are not terribly unphysical. In fact, they look quite nice except for a couple of things:
1. The gap distribution on the Fermi surface shows negative values of the sc gap (in the picture attached you can see it on the colorbar, and I also print the value. It is around -1 meV). Interestingly enough, the gap distribution that I plot on the right panel shows no negative gap values. Maybe it is filtered out by the code automatically.
https://ibb.co/zrSCvLj
2. Another problem I see is in the gap along the imaginary energy axis plot:
https://ibb.co/vHf4f9n
As you can see, at zero energy there are negative values of the sc gap as well.

I am very new to this concept of adding points to the z direction. So could you tell me please if I added enough:
My scf.in file has 24 24 4 grid. My nscf.in file has 12 12 2 grid. Phonons q-grid is 12 12 2.
My interpolation grids are 120 120 4 for both k- and q-grids.

If you have seen such behaviour or know what could have caused it, would you please let me know?

Thank you!
Best regards,
Mikhail

[hpaudya1]

Hi Mikhail,

I am guessing few things based the information you shared.

1. Is your gap calculation conversed? You did not mention the other SC parameters you used for e.g wscut, convergence threshold, mu, temps etc. What value of \lambda did you get? You can plot similarly the \lambda in FS and see if this makes sense.

It would be easy to tell what happened if you could provide the epw input/output files at least.

Best,
Hari Paudyal

[CHILLL]

Hello Hari,

Thank you for your response!
Please find below the input and output files of EPW:
(note that the input file is the one I use as a restart input file to calculate isotropic/anisotropic superconducting properties)

Code: Select all

--
&inputepw
  prefix      = 'mgb2',
  amass(1)    = 24.305,
  amass(2)    = 10.811
  outdir      = './'
  !max_memlt = 6

  ep_coupling = .false. 
  elph        = .false. 
  kmaps       = .true.
  epbwrite    = .false. 
  epbread     = .true. 
  epwwrite    = .false. 
  epwread     = .true. 

  etf_mem     =  1

  nbndsub     =  6 !Number of Wannier functions to utilize
  nbndskip    =  4

  wannierize  = .false.
  num_iter    = 500
  dis_froz_min =   -15
  dis_froz_max  =   -1.0
  proj(1)     = 'Mg:pz'
  proj(2)     = 'B:pz'
  proj(3)     = 'f=0.5,1.0,0.077353794:s'
  proj(4)     = 'f=0.0,0.5,0.077353794:s'
  proj(5)     = 'f=0.5,0.5,0.077353794:s'
  wdata(1)    = 'dis_num_iter = 500'
  wdata(2)    = 'bands_plot = true'                                                              
  wdata(3)    = ' begin kpoint_path'                                                              
  wdata(4)    = 'G 0.000000000 0.000000000 0.000000000 M 0.500000000 0.000000000 0.000000000'
  wdata(5)    = ' M 0.500000000 0.000000000 0.000000000 K 0.333333333 0.333333333 0.000000000'
  wdata(6)    = ' K 0.333333333 0.333333333 0.000000000 G 0.000000000 0.000000000 0.000000000'
  wdata(7)    = 'end kpoint_path'
  iverbosity  = 2

!  parallel_k  = .true.
!  parallel_q  = .false.

  fsthick     = 0.4  ! eV
  eptemp      = 300  ! K
  degaussw    = 0.1  ! eV

  ephwrite    = .false. 
  eliashberg  = .true. 

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

  nsiter   = 500
  conv_thr_iaxis = 1.0d-5

  wscut = 0.5  ! eV

  temps(1) = 8 
 
   muc     = 0.16

  dvscf_dir   = '../phonons/save'

  !band_plot = .true.
  !filqf       = 'mgb2_band.kpt'
  !filkf       = 'mgb2_band.kpt'

 !nscf (Should be commensurate, so watch out!)
  nk1         = 12
  nk2         = 12
  nk3         = 2
 !ph
  nq1         = 12
  nq2         = 12
  nq3         = 2

  !mp_mesh_k = .true.
  nkf1 = 120
  nkf2 = 120
  nkf3 = 4

  nqf1 = 60
  nqf2 = 60
  nqf3 = 4
 /
  38 cartesian ! like in ".dyn0" file!!!
   0.000000000000000E+00   0.000000000000000E+00   0.000000000000000E+00
   0.000000000000000E+00   0.000000000000000E+00  -0.706317380730812E-01
   0.000000000000000E+00   0.962250448649391E-01   0.000000000000000E+00
   0.000000000000000E+00   0.962250448649391E-01  -0.706317380730812E-01
   0.000000000000000E+00   0.192450089729878E+00   0.000000000000000E+00
   0.000000000000000E+00   0.192450089729878E+00  -0.706317380730812E-01
   0.000000000000000E+00   0.288675134594817E+00   0.000000000000000E+00
   0.000000000000000E+00   0.288675134594817E+00  -0.706317380730812E-01
   0.000000000000000E+00   0.384900179459756E+00   0.000000000000000E+00
   0.000000000000000E+00   0.384900179459756E+00  -0.706317380730812E-01
   0.000000000000000E+00   0.481125224324695E+00   0.000000000000000E+00
   0.000000000000000E+00   0.481125224324695E+00  -0.706317380730812E-01
   0.000000000000000E+00  -0.577350269189634E+00   0.000000000000000E+00
   0.000000000000000E+00  -0.577350269189634E+00  -0.706317380730812E-01
   0.833333333333405E-01   0.144337567297409E+00   0.000000000000000E+00
   0.833333333333405E-01   0.144337567297409E+00  -0.706317380730812E-01
   0.833333333333405E-01   0.240562612162348E+00   0.000000000000000E+00
   0.833333333333405E-01   0.240562612162348E+00  -0.706317380730812E-01
   0.833333333333405E-01   0.336787657027287E+00   0.000000000000000E+00
   0.833333333333405E-01   0.336787657027287E+00  -0.706317380730812E-01
   0.833333333333405E-01   0.433012701892226E+00   0.000000000000000E+00
   0.833333333333405E-01   0.433012701892226E+00  -0.706317380730812E-01
   0.833333333333405E-01   0.529237746757165E+00   0.000000000000000E+00
   0.833333333333405E-01   0.529237746757165E+00  -0.706317380730812E-01
   0.166666666666681E+00   0.288675134594817E+00   0.000000000000000E+00
   0.166666666666681E+00   0.288675134594817E+00  -0.706317380730812E-01
   0.166666666666681E+00   0.384900179459756E+00   0.000000000000000E+00
   0.166666666666681E+00   0.384900179459756E+00  -0.706317380730812E-01
   0.166666666666681E+00   0.481125224324695E+00   0.000000000000000E+00
   0.166666666666681E+00   0.481125224324695E+00  -0.706317380730812E-01
   0.166666666666681E+00   0.577350269189634E+00   0.000000000000000E+00
   0.166666666666681E+00   0.577350269189634E+00  -0.706317380730812E-01
   0.250000000000021E+00   0.433012701892226E+00   0.000000000000000E+00
   0.250000000000021E+00   0.433012701892226E+00  -0.706317380730812E-01
   0.250000000000021E+00   0.529237746757165E+00   0.000000000000000E+00
   0.250000000000021E+00   0.529237746757165E+00  -0.706317380730812E-01
   0.333333333333362E+00   0.577350269189634E+00   0.000000000000000E+00
   0.333333333333362E+00   0.577350269189634E+00  -0.706317380730812E-01

And here is the output without the header:

Code: Select all

     ===================================================================
     Solve anisotropic Eliashberg equations
     ===================================================================


     Finish reading .freq file 

                  Fermi level (eV) =    -2.4374773508E+00
     DOS(states/spin/eV/Unit Cell) =     4.7404262616E-01
            Electron smearing (eV) =     1.0000000000E-01
                 Fermi window (eV) =     4.0000000000E-01
     Nr k-points within the Fermi shell =     19204 out of     57600
           2 bands within the Fermi window


     Finish reading .egnv file 


     Max nr of q-points =      4845


     Finish reading .ikmap files


     Size of allocated memory per pool : ~=    1.4911 Gb

     Start reading .ephmat files


     Finish reading .ephmat files 


     Size of allocated memory per pool : ~=    1.4911 Gb

     Size of allocated memory per pool : ~=    1.4911 Gb
     lambda_max =            11.7607030   lambda_k_max =             1.2010538
 
     Electron-phonon coupling strength =    0.5791550
 
     Estimated Allen-Dynes Tc =       4.4930589 K for muc =    0.16000
  
     Estimated BCS superconducting gap =       0.0006814 eV
  
     WARNING WARNING WARNING 
  
     The code will crash for tempsmax much larger than Allen-Dynes Tc
  
     temp(  1) =   8.0000 K 
  
     Solve anisotropic Eliashberg equations on imaginary-axis 
  
     Total number of frequency points nsiw (      1 ) =    115
     Cutoff frequency wscut =     0.5003
  

     Size of allocated memory per pool : ~=    1.4911 Gb

     Size of allocated memory per pool : ~=    1.4914 Gb

     Size of allocated memory per pool : ~=    1.6888 Gb

     Size of required memory per pool : ~=    4.5449 Gb

     AKeri is calculated on the fly since its size exceedes max_memlt

     iter =      1   relerr =     2.4149390072E+00   abserr =     9.5324546168E-04   Znormi(1) =     1.5858699169E+00   Deltai(1) =     6.5783108261E-04
     iter =      2   relerr =     6.9035985106E-01   abserr =     2.0001043748E-04   Znormi(1) =     1.5856404529E+00   Deltai(1) =     8.8699196719E-04
     iter =      3   relerr =     1.3883852598E-01   abserr =     4.5735413357E-05   Znormi(1) =     1.5847890595E+00   Deltai(1) =     1.1205723839E-03
     iter =      4   relerr =     4.1168755869E-01   abserr =     9.6762215191E-05   Znormi(1) =     1.5856293839E+00   Deltai(1) =     8.6991093468E-04
     iter =      5   relerr =     3.6211314899E-01   abserr =     1.3315067396E-04   Znormi(1) =     1.5840441386E+00   Deltai(1) =     1.2927234522E-03
     iter =      6   relerr =     4.7504154481E-02   abserr =     1.8146920708E-05   Znormi(1) =     1.5835801258E+00   Deltai(1) =     1.3625034769E-03
     iter =      7   relerr =     1.3402320521E-01   abserr =     5.9092373634E-05   Znormi(1) =     1.5823914262E+00   Deltai(1) =     1.5880850658E-03
     iter =      8   relerr =     3.0348509456E-01   abserr =     1.9205433781E-04   Znormi(1) =     1.5778580227E+00   Deltai(1) =     2.2219296544E-03
     iter =      9   relerr =     1.3580184439E-01   abserr =     9.8248380125E-05   Znormi(1) =     1.5765389919E+00   Deltai(1) =     2.3760213208E-03
     iter =     10   relerr =     7.6113887277E-02   abserr =     5.5496075427E-05   Znormi(1) =     1.5759773073E+00   Deltai(1) =     2.5098007463E-03
     iter =     11   relerr =     7.7798073064E-02   abserr =     6.0936240731E-05   Znormi(1) =     1.5739728923E+00   Deltai(1) =     2.7555820995E-03
     iter =     12   relerr =     3.4684463438E-02   abserr =     2.6510588374E-05   Znormi(1) =     1.5740871757E+00   Deltai(1) =     2.7430654450E-03
     iter =     13   relerr =     1.2088660425E-01   abserr =     1.0470768327E-04   Znormi(1) =     1.5720970304E+00   Deltai(1) =     2.9854996920E-03
     iter =     14   relerr =     5.0718530702E-02   abserr =     4.6275843782E-05   Znormi(1) =     1.5709477762E+00   Deltai(1) =     3.1158908871E-03
     iter =     15   relerr =     2.0202485643E-02   abserr =     1.8795764716E-05   Znormi(1) =     1.5705720563E+00   Deltai(1) =     3.1507074713E-03
     iter =     16   relerr =     3.2595770807E-02   abserr =     3.1178174976E-05   Znormi(1) =     1.5694844113E+00   Deltai(1) =     3.2800200112E-03
     iter =     17   relerr =     1.2940404886E-02   abserr =     1.2533245586E-05   Znormi(1) =     1.5691037222E+00   Deltai(1) =     3.3260687048E-03
     iter =     18   relerr =     7.1936860172E-03   abserr =     7.0172628516E-06   Znormi(1) =     1.5689270181E+00   Deltai(1) =     3.3423971161E-03
     iter =     19   relerr =     2.6249962400E-02   abserr =     2.6294725223E-05   Znormi(1) =     1.5682624009E+00   Deltai(1) =     3.4107577162E-03
     iter =     20   relerr =     1.1975952614E-02   abserr =     1.2140231173E-05   Znormi(1) =     1.5678799347E+00   Deltai(1) =     3.4495395974E-03
     iter =     21   relerr =     4.9650721200E-03   abserr =     5.0462332489E-06   Znormi(1) =     1.5676795442E+00   Deltai(1) =     3.4660649428E-03
     iter =     22   relerr =     8.4127112994E-03   abserr =     8.6209179893E-06   Znormi(1) =     1.5674329618E+00   Deltai(1) =     3.4944376710E-03
     iter =     23   relerr =     9.8573247077E-03   abserr =     1.0196308179E-05   Znormi(1) =     1.5672702109E+00   Deltai(1) =     3.5120173634E-03
     iter =     24   relerr =     5.5341026096E-03   abserr =     5.7416192747E-06   Znormi(1) =     1.5670649729E+00   Deltai(1) =     3.5304334929E-03
     iter =     25   relerr =     3.4929710522E-03   abserr =     3.6358013890E-06   Znormi(1) =     1.5670143089E+00   Deltai(1) =     3.5362057705E-03
     iter =     26   relerr =     3.7988337392E-03   abserr =     3.9619036914E-06   Znormi(1) =     1.5668773861E+00   Deltai(1) =     3.5486926176E-03
     iter =     27   relerr =     2.9946488102E-03   abserr =     3.1325603953E-06   Znormi(1) =     1.5667915443E+00   Deltai(1) =     3.5569280904E-03
     iter =     28   relerr =     1.7476864080E-03   abserr =     1.8312189525E-06   Znormi(1) =     1.5667265647E+00   Deltai(1) =     3.5632372332E-03
     iter =     29   relerr =     3.8336330191E-03   abserr =     4.0316165562E-06   Znormi(1) =     1.5666525243E+00   Deltai(1) =     3.5711731088E-03
     iter =     30   relerr =     2.3128694137E-03   abserr =     2.4306039116E-06   Znormi(1) =     1.5666277812E+00   Deltai(1) =     3.5728364064E-03
     iter =     31   relerr =     2.3196250308E-03   abserr =     2.4431308205E-06   Znormi(1) =     1.5665829220E+00   Deltai(1) =     3.5775338228E-03
     iter =     32   relerr =     1.6071388661E-03   abserr =     1.6919763151E-06   Znormi(1) =     1.5665631940E+00   Deltai(1) =     3.5790124954E-03
     iter =     33   relerr =     1.0651249882E-03   abserr =     1.1225305266E-06   Znormi(1) =     1.5665255844E+00   Deltai(1) =     3.5826173728E-03
     iter =     34   relerr =     2.1171338369E-04   abserr =     2.2317102367E-07   Znormi(1) =     1.5665195517E+00   Deltai(1) =     3.5832486883E-03
     iter =     35   relerr =     6.9534533825E-04   abserr =     7.3348014434E-07   Znormi(1) =     1.5664950234E+00   Deltai(1) =     3.5855615332E-03
     iter =     36   relerr =     1.9162314851E-04   abserr =     2.0216916500E-07   Znormi(1) =     1.5664914838E+00   Deltai(1) =     3.5859385533E-03
     iter =     37   relerr =     3.6454924866E-04   abserr =     3.8475142515E-07   Znormi(1) =     1.5664791444E+00   Deltai(1) =     3.5871295782E-03
     iter =     38   relerr =     1.1154268282E-04   abserr =     1.1773643939E-07   Znormi(1) =     1.5664771379E+00   Deltai(1) =     3.5873378753E-03
     iter =     39   relerr =     3.4306141691E-04   abserr =     3.6223404219E-07   Znormi(1) =     1.5664659399E+00   Deltai(1) =     3.5884573775E-03
     iter =     40   relerr =     1.9288604924E-04   abserr =     2.0369228515E-07   Znormi(1) =     1.5664659499E+00   Deltai(1) =     3.5885206656E-03
     iter =     41   relerr =     2.3728118589E-04   abserr =     2.5059351266E-07   Znormi(1) =     1.5664585740E+00   Deltai(1) =     3.5891611158E-03
     iter =     42   relerr =     1.1699095607E-04   abserr =     1.2356901508E-07   Znormi(1) =     1.5664547578E+00   Deltai(1) =     3.5895188470E-03
     iter =     43   relerr =     7.9943869059E-05   abserr =     8.4436310871E-08   Znormi(1) =     1.5664540265E+00   Deltai(1) =     3.5895637161E-03
     iter =     44   relerr =     1.4496535939E-04   abserr =     1.5313360713E-07   Znormi(1) =     1.5664505482E+00   Deltai(1) =     3.5899237669E-03
     iter =     45   relerr =     4.8277943391E-05   abserr =     5.1000655799E-08   Znormi(1) =     1.5664489010E+00   Deltai(1) =     3.5900790627E-03
     iter =     46   relerr =     4.2524589653E-05   abserr =     4.4924666924E-08   Znormi(1) =     1.5664472862E+00   Deltai(1) =     3.5902309725E-03
     iter =     47   relerr =     3.8781024317E-05   abserr =     4.0971400695E-08   Znormi(1) =     1.5664462219E+00   Deltai(1) =     3.5903354781E-03
     iter =     48   relerr =     1.8550256392E-05   abserr =     1.9598283781E-08   Znormi(1) =     1.5664453962E+00   Deltai(1) =     3.5904101467E-03
     iter =     49   relerr =     1.9840790994E-05   abserr =     2.0962144530E-08   Znormi(1) =     1.5664447588E+00   Deltai(1) =     3.5904703702E-03
     iter =     50   relerr =     1.2426015630E-05   abserr =     1.3128461813E-08   Znormi(1) =     1.5664442921E+00   Deltai(1) =     3.5905132946E-03
     iter =     51   relerr =     1.1814405423E-05   abserr =     1.2482424067E-08   Znormi(1) =     1.5664439001E+00   Deltai(1) =     3.5905501071E-03
     iter =     52   relerr =     8.8377204926E-06   abserr =     9.3375116850E-09   Znormi(1) =     1.5664436567E+00   Deltai(1) =     3.5905743014E-03
     Convergence was reached in nsiter =     52

     Size of allocated memory per pool : ~=    1.5901 Gb
  
     iaxis_imag   :  45080.01s CPU  45844.55s WALL (       1 calls)

     Size of allocated memory per pool : ~=    1.4913 Gb
     itemp =   1   total cpu time :          45844.55 secs
 
     Unfolding on the coarse grid
 
     INITIALIZATION: 
 
     init_vloc    :      0.23s CPU      0.24s WALL (       1 calls)
     init_us_1    :      0.03s CPU      0.03s WALL (       1 calls)
 
 
     Electron-Phonon interpolation
 
 
     ELIASHBERG   :  46184.84s CPU  46980.88s WALL (       1 calls)
 
     Total program execution
     EPW          :     12h49m CPU     13h 3m WALL

                                                                                          
 Please consider citing:                                                                  
 S. Ponce, E. R. Margine, C. Verdi and F. Giustino, Comput. Phys. Commun. 209, 116 (2016) 
                                                                                          
 In addition, if you used anisotropic Eliashberg superconductivity please cite:           
              E. R. Margine and F. Giustino, Phys. Rev. B 87, 024505 (2013)               
              if you used transport properties (scattering rates, mobility) please cite:  
              S. Ponce, E. R. Margine and F. Giustino, Phys. Rev. B 97, 121201 (2018)    

I can't find anything bad in the isotropic results. The coupling values are realistic and so is the isotropic Tc. If there is anything else I can provide, please let me know.

Best regards,
Mikhail

[roxana]

Hi,

You could try to run the anisotropic calculations at lower temperatures than 8 K. I see that the estimated Allen-Dynes Tc is just above 4 K.

Can you also provide a plot for gap versus T from the isotropic calculations?

Finally, I would recommend you use the latest version of the code.

Best,
Roxana

[CHILLL]

Hello,

Thank you for your answer!

I tried anisotropic calculation at 3.5 K, and the problem persists.
I performed isotropic calculations too.
If I do only .liso. = true calculations, my jobs crash after I exceed the isotropic critical temperature (Allen-Dynes is around 4.5 K).
Isotropic gap VS temperature is here: https://ibb.co/2FkzPqw (it is still non-zero even at 4.5 K, but at least it seems to be going down)

Now, when I was doing anisotropic calculations with laniso = .true., I get non-zero isotropic gap at higher temperatures. For example, I have a file "mgb2.imag_iso_008.00" at 8 K, and the isotropic gap value there is 3.5905743 meV, which is significantly higher that all the values I got in my Isotropic gap VS temperature plot. I never really checked what should be the value of the isotropic gap when you do anisotropic calculations at temperatures much higher than isotropic Tc.

Is this behaviour normal?

Best regards,
Mikhail

[roxana]

Hi,

Regarding your question for liso=.true. The Tc obtained with the isotropic calculations is in general close to the value given by the Allen-Dynes formula but almost never exactly the same. If you want to better resolve the gap close to Tc you need to take smaller steps in temperature of 0.1 K since the converge of self-consistently loop becomes less stable in that region. You should also show the plot with the energy axis starting from 0.

Regarding you question for laniso=.true. The isotropic gap in this case is an average of the anisotropic gap points \Delta_nk and can be very different than the isotropic gap from liso=.true..

Best,
Roxana

[CHILLL]

Thank you for your response !

"You should also show the plot with the energy axis starting from 0". Is this something you want me to provide? Could you please tell me what exactly you mean by that?

Would you recommend to check something else? It seems to me that isotropically everything is alright, and it is just the anisotropic calculation that is problematic for this material.

Best,
Mikhail

[LiuHD]

Hello,
We also face the same problems that some negative gaps emerge.

Could you tell us how you solved this problem?

We will sincerely appreciate the help you provide.

Best Wishes.