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Allen dynes formula for Tc is not giving correct lambda from epw calcs
Posted: Wed Dec 11, 2024 8:08 am
by simba2828
Dear EPW Experts,
I am running one anisotropic superconducting calculation where the calculation gives the following output in epw.out file:
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......
a2f file is found and will be used to estimate initial gap
Finish reading a2f file
Electron-phonon coupling strength = 1.6514433
Estimated Allen-Dynes Tc = 3.105056 K for muc = 0.10000
Estimated w_log in Allen-Dynes Tc = 2.153136 meV
Estimated BCS superconducting gap = 0.470929 meV
Estimated Tc from machine learning model = 4.895778 K
.......
With this given lambda (el-ph strength)=1.6514433, w_log= 2.153136 meV and mu*=0.1, I am not getting Tc= 3.105056 K. Could anyone clarify where I am misinterpreting? Is this lambda (1.6514433), given by Migdal-Eliashberg approach, is different from Allen-dynes lambda? Or w_log is something different?
I am attaching a figure where the Allen-Dynes formula for Tc is given.
Thank you for your response.
Sincerely,
Shubham
Re: Allen dynes formula for Tc is not giving correct lambda from epw calcs
Posted: Wed Dec 11, 2024 11:18 am
by simba2828
I noticed that w_log is in meV while it should be in Kelvin. Could anyone tell what is the conversion formula for logarithmic average of omega? Is it E = kB.T?
Also, I noticed that from QE calculations I am getting lambda close to 1 while EPW gives 1.65. Why there is a discrepancy?
Additionally, a2F.dos also print lambda at the end of the file which is 0.77, again a discrepancies. Which one should I consider?
Output of the `lambda` file:
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Electron-phonon coupling constant, lambda
Broadening 0.0200 lambda 0.9669 dos(Ef) 23.4848 omega_ln [K] 52.2538
Broadening 0.0400 lambda 0.8246 dos(Ef) 22.8038 omega_ln [K] 57.1286
Broadening 0.0600 lambda 0.8655 dos(Ef) 20.8352 omega_ln [K] 52.5826
Broadening 0.0800 lambda 0.9878 dos(Ef) 19.8054 omega_ln [K] 46.4001
Broadening 0.1000 lambda 1.0742 dos(Ef) 19.6655 omega_ln [K] 43.4068
Broadening 0.1200 lambda 1.0882 dos(Ef) 20.0924 omega_ln [K] 42.8778
Broadening 0.1400 lambda 1.0565 dos(Ef) 20.8684 omega_ln [K] 43.8291
Broadening 0.1600 lambda 1.0120 dos(Ef) 21.8472 omega_ln [K] 45.6556
Broadening 0.1800 lambda 0.9726 dos(Ef) 22.9001 omega_ln [K] 47.8655
Broadening 0.2000 lambda 0.9425 dos(Ef) 23.9120 omega_ln [K] 50.0714
Re: Allen dynes formula for Tc is not giving correct lambda from epw calcs
Posted: Fri Dec 13, 2024 9:43 pm
by Shashi
Dear Subham,
The w_log unit in EPW is indeed correct and expressed in meV. When converted to Kelvin, w_log is 24.976 K. The w_log expression depends on electron-phonon coupling strength, which differs between EPW and QE in your case giving differences in w_log values. Using your formula, I estimated the Tc to be 3.1038 K, which matches exactly with the Tc printed in EPW output. Please recheck.
Regarding the discrepancy in electron-phonon coupling strength values between QE and EPW, it could likely be attributed to differences between k and q-grid sizes. Typically, QE uses coarser grids, whereas EPW relies on much finer grid sizes. You can also look at the paper by Hitoshi (Phy. Rev. B 110, 064505 (2024)), where he showed for Pb (Table 2) that the electron-phonon coupling strengths differ with grid sizes.
Regards,
Shashi
Re: Allen dynes formula for Tc is not giving correct lambda from epw calcs
Posted: Sat Dec 14, 2024 6:08 pm
by simba2828
Dear Shashi,
Thank you for your reply and the reference. But isn't lambda is very large? In this paper by Allen and Dynes: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.12.905 , it has been explained whenever lambda > 1.5 there is correction factor used in Allen dynes Tc. Is that factor taken into account for the EPW calculations which can explain lambda 1.65?
Thank you again.
Shubham
Re: Allen dynes formula for Tc is not giving correct lambda from epw calcs
Posted: Mon Dec 16, 2024 12:09 am
by Shashi
Dear Subham,
The paper you mentioned discusses the scenarios for asymptotic Tc in the case of lambda < 1 and lambda > 1 in Sec. III. To clarify, there is no additional factor applied in EPW for calculating Allen-Dynes' Tc, and the equation used in EPW is the same as the one you shared. If you wish to obtain more accurate Tc values, I would recommend solving the Eliashberg equations, either using the isotropic or anisotropic formalism in EPW. This approach might be better to compare Tc with your semi-empirical estimation.
Regards,
Shashi
Re: Allen dynes formula for Tc is not giving correct lambda from epw calcs
Posted: Mon Dec 16, 2024 2:07 pm
by simba2828
Thank you Shashi for the clarification.