Can Fermi levels be specified to calculate a2F(superconducting gap)

[dhw]

Hello administrator:
I encountered a problem when I used EPW to calculate the electro-acoustic coupling strength. The output file will output a Fermi level after the epw.x calculation, but the Fermi level in Self consistent calculation is quite different from the epw.x output.
The Self-consistent output (fermi level):

the Fermi energy is 2.9974 ev

the epw. X output (fermi level):

DOS = 1.280437 states/spin/eV/Unit Cell at Ef= 3.000886 eV

In the recent calculation of another system, the Fermi energy level difference between Wannier fitting and self-consistent output was 1.0eV, which made the calculation of a2F inaccurate, so the following test was carried out. The following two tests were carried out using the system corresponding to the previous calculation of Fermi energy levels. However, the results of a2F vary greatly. May I ask whether my test here is useful? Can the EPw.x calculation of a2F be calculated by specifying Fermi levels in the input file?
Here are the input files for the two tests (the calculated input files for PW.x are the same) :
test1:
input file of epw.x

&inputepw
outdir = './outdir/'
ep_coupling = .true.
elph = .true.
kmaps = .false.
epwwrite = .true.
epwread = .false.
wannierize = .true.
! num_iter = 0
dis_froz_min= 2.0
dis_froz_max= 4.0
proj(1) = 'Mo:l=1;l=2'
wdata(1) = 'Begin Kpoint_Path'
wdata(2) = 'G 0.00 0.00 0.00 M 0.00 0.50 0.00'
wdata(3) = 'M 0.00 0.50 0.00 K 0.333 0.333 0.00'
wdata(4) = 'K 0.333 0.333 0.0 G 0.00 0.00 0.00'
wdata(5) = 'End Kpoint_Path'
wdata(6) = 'bands_plot = .true.'
wdata(7) = 'bands_num_points = 55'
wdata(8) = 'guiding_centres = .true.'
wdata(9) = 'dis_num_iter = 5000'
bands_skipped = 'exclude_bands = 1:12'

system_2d=.true.
etf_mem = 1
nbndsub = 16 ! Lowest boundary for the phonon frequency
ephwrite = .false. ! Writes .ephmat files used when Eliasberg = .true.
fsthick = 0.1 ! eV
degaussw = 0.01 ! eV
nsmear = 1
nqsmear = 1
delta_smear = 0.01 ! eV
degaussq = 0.5 ! meV
nqstep = 500
! eliashberg = .true.
! laniso = .true.
! limag = .true.
! lpade = .true.
conv_thr_iaxis = 1.0d-4
! max_memlt = 3.0d0
! asr_typ = 'crystal'
delta_approx = .true.,
! elecselfen = .true.,
phonselfen = .true.,
a2f = .true. ,
wscut = 1.0 ! eV Upper limit over frequency integration/summation in the Elisashberg eq
! nstemp = 12 ! Nr. of temps
! temps = 2.00 13.00 ! K provide list of temperetures OR (nstemp and temps = tempsmin tempsmax for even space mode)
nsiter = 500
muc = 0.20876
dvscf_dir = '../phonon/save'

nk1 = 12
nk2 = 12
nk3 = 1
nq1 = 6
nq2 = 6
nq3 = 1

! mp_mesh_k = .true.
nkf1 = 120
nkf2 = 120
nkf3 = 1
nqf1 = 60
nqf2 = 60
nqf3 = 1
/

output **.a2f.01

87.2111998 0.0000000
87.3863227 0.0000000
87.5614456 0.0000000
Integrated el-ph coupling
# 0.6672296
Phonon smearing (meV)
# 0.5000000
Electron smearing (eV) 0.0100000
Fermi window (eV) 0.1000000
Summed el-ph coupling 0.6604335

test2:
input file of epw.x

&inputepw
outdir = './outdir/'
ep_coupling = .true.
elph = .true.
kmaps = .false.
epwwrite = .true.
epwread = .false.
wannierize = .true.
! num_iter = 0
dis_froz_min= 2.0
dis_froz_max= 4.0
proj(1) = 'Mo:l=1;l=2'
wdata(1) = 'Begin Kpoint_Path'
wdata(2) = 'G 0.00 0.00 0.00 M 0.00 0.50 0.00'
wdata(3) = 'M 0.00 0.50 0.00 K 0.333 0.333 0.00'
wdata(4) = 'K 0.333 0.333 0.0 G 0.00 0.00 0.00'
wdata(5) = 'End Kpoint_Path'
wdata(6) = 'bands_plot = .true.'
wdata(7) = 'bands_num_points = 55'
wdata(8) = 'guiding_centres = .true.'
wdata(9) = 'dis_num_iter = 5000'
bands_skipped = 'exclude_bands = 1:6'

system_2d=.true.
etf_mem = 1
nbndsub = 16 ! Lowest boundary for the phonon frequency
ephwrite = .false. ! Writes .ephmat files used when Eliasberg = .true.
fsthick = 0.1 ! eV
degaussw = 0.01 ! eV
nsmear = 1
nqsmear = 1
delta_smear = 0.01 ! eV
degaussq = 0.5 ! meV
nqstep = 500
efermi_read = .true.
fermi_energy = 3.000886
! eliashberg = .true.
! laniso = .true.
! limag = .true.
! lpade = .true.
conv_thr_iaxis = 1.0d-4
! max_memlt = 3.0d0
! asr_typ = 'crystal'
delta_approx = .true.,
! elecselfen = .true.,
phonselfen = .true.,
a2f = .true. ,
wscut = 1.0 ! eV Upper limit over frequency integration/summation in the Elisashberg eq
! nstemp = 12 ! Nr. of temps
! temps = 2.00 13.00 ! K provide list of temperetures OR (nstemp and temps = tempsmin tempsmax for even space mode)
nsiter = 500
muc = 0.20876
dvscf_dir = '../../../phonon/save'

nk1 = 12
nk2 = 12
nk3 = 1
nq1 = 6
nq2 = 6
nq3 = 1

! mp_mesh_k = .true.
nkf1 = 120
nkf2 = 120
nkf3 = 1
nqf1 = 60
nqf2 = 60
nqf3 = 1
/

output **.a2f.01

87.2111998 0.0000000
87.3863227 0.0000000
87.5614456 0.0000000
Integrated el-ph coupling
# 0.7338264
Phonon smearing (meV)
# 0.5000000
Electron smearing (eV) 0.0100000
Fermi window (eV) 0.1000000
Summed el-ph coupling 0.7271920

In addition, I would like to ask you a question: after wannier fitting is well calculated, how to adjust the Fermi energy level output of EPw. x to be inconsistent with the self-consistent output? Thank you

[hpaudya1]

Hi dhw,

A few meV difference in Fermi energies calculated in coarse grid (nscf run) and fine mesh (epw run) is expected (because of different k-meshes used). If you want to compare the Fermi energies between pw and epw calculation, you need to make a test nscf calculation on the same mesh that you have used in the epw calculation, and I think you will get comparable values.

Can the EPw.x calculation of a2F be calculated by specifying Fermi levels in the input file?

Yes, use "efermi_read = .true." and "fermi_energy = XXX" (XXX: value of the Fermi energy you want to use in eV) two flags in your input file.

I hope it helps.

Happy EPWing,
Hari Paudyal

[dhw]

Hi Hari Paudyal :
I am glad to receive your reply to me. But I still have my doubts.
According to your answer:

Yes, use "efermi_read = .true." and "fermi_energy = XXX" (XXX: value of the Fermi energy you want to use in eV) two flags in your input file.

but the a2f output calculated by EPW after I specified it is different from that not specified, and the difference is still a little big (5.8%). You mean to specify Fermi levels only if the Fermi levels output by EPW after wannier fitting are close to self-consistent ? As for the two input files posted in my question, the specified and unspecified tests after adjusting the band number excluded during Wannier fitting show that **.a2f file results are inconsistent. Is the problem caused by the inconsistent band number excluded?

[hlee]

Dear dhw:

Is the problem caused by the inconsistent band number excluded?

Yes, I guess so; you excluded 6 bands in one calculation, but excluded 12 bands in the other calculation. This means you are considering the different band manifold for Wannierization.

So I think that in order to make more consistent comparison, you need to exclude the same number of bands in two cases.

PS) The number of excluded bands also affects the number of electrons in EPW which is used in the evaluation of the Fermi energy in EPW. But, in your 2nd example, you specified the Fermi energy and in this case the number of electrons (the variable of nelec in EPW) is not considered.

Sincerely,

Hyungjun Lee

[dhw]

hello Hyungjun Lee :

PS) The number of excluded bands also affects the number of electrons in EPW which is used in the evaluation of the Fermi energy in EPW. But, in your 2nd example, you specified the Fermi energy and in this case the number of electrons (the variable of nelec in EPW) is not considered.

you said that by specifying the Fermi level you don't take into account the change in the number of electrons, so I have the following questions, and I hope you can guide me further if you are clear:

• Example 2 specifies that the Fermi level is equal to the Fermi level output of EPW of TEST 1, and then calculates if A2f should be consistent with example 1 ?

• If (1) is not correct, it is proved that the Fermi level designation cannot correctly output the electro-acoustic coupling constant at the Fermi level of the system?

• Finally, does the calculation of the electro-acoustic coupling coefficient A2f necessarily require that the Fermi levels obtained by Epw calculation fit with the self-consistent one

Sincerely,

[hlee]

Dear dhw:

I think that if two inputs are exactly the same except for the excluded bands and the specification of the Fermi energy and if you use the same excluded bands and the same Fermi energy as the one calculated on fine grids in test 1, you should obtain the (almost) same result.

Also, as Hari said, the Fermi energy depends on the density of k grids and since you used the different k grids, it is likely to have the different Fermi energy on fine grids from the one from scf runs.

Sincerely,

H. Lee

[dhw]

Dear,H. Lee:
I wonder if I can understand it this way? It is clear to me that the Fermi level of epW output depends on frequency band exclusion. So the Fermi levels I need to specify can only be specified if EPW outputs the correct Fermi levels (here the correct Fermi levels are roughly the same as the self-consistent output, i.e. not much different)?

Sincerely,
dhw