How to plot Eliashberg function alpha2F(w) and EPC strength (lambda) together in one plot ?

[sahildani]

Dear all,
I am using Quantum Espresso version 6.4.1 and trying to find superconducting parameters of CoO2 by following Example of Pb (Tutorial Tue.5). I am able to generate all the files but I am not getting how to plot Eliashberg function alpha2F(w) and EPC strength (lambda) together in one single plot. I am going through the literature and people had plotted these two parameters in a one single plot w.r.t. frequency.

c9nr03954f-f3_hi-res.gif (89.14 KiB) Viewed 5820 times

We need to plot a2F.dosX (X is broadening) for producing Eliasheberg function (alpha2F(w)). In this file there is only one single value of lambda, so when I am plotting them together, I am just getting a single line instead of accumulated EPC strength λ(ω). I have attached my a2F.dos1 file, please find it. Is the last column in this file denotes the λ(ω)?

Screenshot (73).png (156.54 KiB) Viewed 5820 times

Screenshot (72).png (151.95 KiB) Viewed 5820 times

Also how to plot phonon dispersion with linewidth. Do we need to plot elph.gamma.X file for that ?

I have also followed PHonon/example/tetra_example. So I wanted to know out of these two methods which one is the best one.
I am a beginner in this field. So any suggestion would be very helpful.
Hoping to hear from you.
Thank you.
Regards
Sahil Dani
Research Scholar, IIT Ropar INDIA.

[gkafle1]

Hi Sahil Dani,

In order to get the plot you want, one needs to plot the second column of a2f.dosX (X is broadening) for the Eliashberg spectral function (a2f). As you see in the header of your attached file, the first column of a2f.dosX is the frequency (w) and the second column is a2f; the rest of the columns are a2f for each mode. I believe Quantum Espresso does not print the integrated λ(ω), however, you can write a small code to integrate lambda based on the data of the a2f.dosX file as in the attached png file.

One thing to mention, when you use EPW code for the electron-phonon calculation, you will get a prefix.a2f file where both the a2f and integrated lambda are printed, and you can get the plot as you want easily.

For the phonon dispersion and linewidth, please follow the following tutorial
https://indico.ictp.it/event/8301/sessi ... al/0/0.pdf

Thank you!

Best
Gyanu Kafle
Binghamton University, USA

[hpaudya1]

Hi Sahil,

I would recommend going through this tutorial https://epwdoc.gitlab.io/source/doc/MgB2.html step by step where I have explained all the file formats and the way to plot them. In addition, I recommend using the latest version (QE-v7.1) of the code where we have updated many things.

Best,
Hari

[sahildani]

Dear all,

Thank you for the suggestions.
I had used Origin to plot lambda and alpha2F(w) together and getting results now. Please find the attachment.

a2f1.jpg (57.19 KiB) Viewed 5771 times

I wanted to ask few more things.
The lambda must be the higher value (2.12) that I am getting from this plot?
But this value is different from the values in lambda.out file,

Screenshot (75).png (117.45 KiB) Viewed 5771 times

and same as we are getting in lambda file.

Screenshot (76).png (99.78 KiB) Viewed 5771 times

I think they need not to be same, because one of them is electron-phonon coupling strength and other one is electron-phonon mass enhancement parameter. Then which value should be consider as el-ph coupling strength.
Also in lambda.out file, I get a number of Tc values, lambda, and omega_log values at different degauss values. So how to decide which Tc value should I take?
Is it something related to the broadening (degauss) value that I took for plotting a2F(w) v/s w. Should I take that same broadening for getting the Tc value from lambda.out file.
Or should I take lambda value from plot and look for that value in lambda.out file and take the corresponding Tc value.

Hoping for a response.
Thank you
Regards
Sahil Dani

[gkafle1]

Hi Sahil,
It's good to hear that you are able to plot a2f and λ(ω) in the same plot.

As far as I understand, the data printed in lambda.out (or lambda.dat) is calculated by reading the lambda values for each q and each mode from the elph.inp_lambda.XX files and summing over q-points as seen in the following subroutine:
https://gitlab.com/QEF/q-e/-/blob/devel ... lambda.f90

The lambda values for each q and each mode in the elph.inp_lambda.XX files are calculated using the Eqn (3) of Appendix-A of the following user guide
https://www.quantum-espresso.org/wp-con ... _guide.pdf

So, I think you can take the λ value from the lambda.out (or lambda.dat) file.

Regarding your question on "how to decide which Tc value should I take", in my experience, I never get a converged lambda and Tc as a function of broadening using Quantum Espresso, so it's hard to tell which values should you take. Maybe you can try to match the λ value from the experiment if available.

Best
Gyanu Kafle