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Different values of lambda and Tc (iso vs aniso?) 
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Joined: Thu May 26, 2016 11:27 am
Posts: 5
Post Different values of lambda and Tc (iso vs aniso?)
Dear all,

I am calculating lambda using two different methods implemented in EPW.

First one is obtained by activating anisotropic Eliashberg equation related tags.

Code:
  eliashberg  = .true.
  laniso = .true.
  limag = .true.
  lpade = .true.


The result is as below:

Code:
     ===================================================================
     Solve anisotropic Eliashberg equations
     ===================================================================


     Finish reading .freq file

                  Fermi level (eV) =     1.4490810867E+00
     DOS(states/spin/eV/Unit Cell) =     7.4601791612E-01
            Electron smearing (eV) =     1.0000000000E-01
                 Fermi window (eV) =     4.0000000000E-01
     Nr irreducible k-points within the Fermi shell =       134 out of       231
           2 bands within the Fermi window


     Finish reading .egnv file


     Max nr of q-points =       466


     Finish reading .ikmap files


     Start reading .ephmat files


     Finish reading .ephmat files

     lambda_max =             1.3814131   lambda_k_max =             0.7463819

     Electron-phonon coupling strength =    0.5890385

     Estimated Allen-Dynes Tc =       1.0488626 K for muc =    0.16000
 
     Estimated BCS superconducting gap =       0.0001591 eV


and the second one is obtained by activating a2f tags and deactivating anisotropic Eliashberg tags.

Code:
  a2f = .true.
  phonselfen = .true.


The result is as below:

Code:
     ===================================================================
     Eliashberg Spectral Function in the Migdal Approximation
     ===================================================================

     lambda :    0.5689812
     lambda_tr :    0.7333977

     Estimated Allen-Dynes Tc

     logavg =    0.0006900 l_a2F =    0.5735213
     mu =   0.10 Tc =         2.164145346702 K
     mu =   0.12 Tc =         1.691229225724 K
     mu =   0.14 Tc =         1.276401502717 K
     mu =   0.16 Tc =         0.922975116778 K
     mu =   0.18 Tc =         0.632737937327 K
     mu =   0.20 Tc =         0.405375457882 K


The lambda obtained by the first one is 0.5890385, while the lambda from the second method is 0.5689812. and T_c is also slightly different.

Could it be understood it is because of the effect of anisotropic nature of the system? or some bugs in the code or numerical inaccuracy? I've calculated the second part by re-loading previously obtained files that required solving the Eliashberg equation. Any comments would be helpful and appreciate.

Best regards,
Jun-Ho


Fri Jan 04, 2019 9:09 am
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 112
University: SUNY-Binghamton
Post Re: Different values of lambda and Tc (iso vs aniso?)
Dear Jun-Ho,

The reason that the two values are slightly different is because they are calculated using different formulas.

1) For the default setting

a2f = .true.
phonselfen = .true.

the e-ph coupling strength is calculated using the imaginary part of the phonon self-energy [Eq. 9 in Computer Physics Communications 209, 116 (2016)]. In this case \lambda= Im[\Pi_{q\nu}] / [\pi N_F \omega^2_{q\nu}].

2) If you set

delta_approx = .true.

together with

a2f = .true.
phonselfen = .true.

the e-ph coupling strength will be calculated using the double delta approximation [Eq. 11 in Computer Physics Communications 209, 116 (2016)]. This second approach is also used when calculating the e-ph coupling strength with the flag eliashberg=.true.

Just a note, the T_c value are going to be different when solving the Eliashberg equations with laniso=.true. or liso=.true.

Best,
Roxana

_________________
Roxana Margine
Assistant Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Fri Jan 04, 2019 2:24 pm
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Joined: Thu May 26, 2016 11:27 am
Posts: 5
Post Re: Different values of lambda and Tc (iso vs aniso?)
Dear Roxana,

Thank you very much for your reply.

Does the significant difference between the calculated values of lambda obtained by two different methods mean that these are not converged results with respect to fine k- or q-grids?

Best regards,
Jun-Ho


Sat Jan 05, 2019 5:13 am
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 112
University: SUNY-Binghamton
Post Re: Different values of lambda and Tc (iso vs aniso?)
Hi Jun-Ho,

I think the difference you are seeing is not that large, but you should always check how the value for lambda changes with respect to k- and q-grids regardless of the method you use.

Best,
Roxana

_________________
Roxana Margine
Assistant Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Sat Jan 05, 2019 4:43 pm
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Joined: Thu May 26, 2016 11:27 am
Posts: 5
Post Re: Different values of lambda and Tc (iso vs aniso?)
Thank you very much!

Best,
Jun-Ho


Wed Jan 09, 2019 12:36 am
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Joined: Thu Nov 29, 2018 9:02 am
Posts: 22
University: Institute of Physics
Post Re: Different values of lambda and Tc (iso vs aniso?)
I calculate phonon selfenergy with and without delta_approx.
And I get different result,I want to ask which one is accurate?
Should I use delta_approx. when I calculate a2F,lambda and Tc?
Image


Last edited by liu xinbao on Mon Mar 18, 2019 6:06 am, edited 3 times in total.

Thu Mar 14, 2019 3:07 am
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 112
University: SUNY-Binghamton
Post Re: Different values of lambda and Tc (iso vs aniso?)
Hi,

Both expressions for are correct, it depends what you are using them for. The double delta approximation is generally used to estimate a2f, lambda, and Tc for superconductors.

Best,
Roxana

_________________
Roxana Margine
Assistant Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Fri Mar 15, 2019 11:06 pm
Profile

Joined: Thu Nov 29, 2018 9:02 am
Posts: 22
University: Institute of Physics
Post Re: Different values of lambda and Tc (iso vs aniso?)
Thank you very much,roxana


Mon Mar 18, 2019 6:02 am
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