EPW Forum

Dear EPW developers,
I have a general question about superconductors with no inversion symmetry. EPW is based on Migdal-Eliashberg theory (ME theory). If I plan to study a metal or a doped semiconductor with broken inversion symmetry, may I still use ME theory (implemented in EPW) to calculate its electron-phonon coupling, Eliashberg spectral function and estimate superconducting Tc with McMillan's formula?
I did some tests in an artificial system with broken inversion symmetry and EPW ran properly and generated electron-phonon coupling and estimated Tc. But my concern is that as far as l understand, BCS-ME theory is only applicable to systems with inversion symmetry. Therefore I am wondering whether EPW can in principle calculate superconductors with no inversion symmetry?
Thank you very much for your help. We greatly appreciate that.
Best regards.

Dr. Hanghui Chen
Department of Physics
NYU Shanghai and New York University

Hi,

I am not aware of any constrain in the BCS-ME theory to restrict its applicable only to systems with inversion symmetry. If you know a study where this is discussed, could you please send the reference?

Best,
Roxana

Dear Roxana,
Thank you very much for your reply. After posting my inquiry, I also consulted some other professors and found that my understanding of BCS-ME theory is not accurate. Anisotropic ME theory can be applied to superconductors without an inversion symmetry. I am sorry for the confusion.
However, on a related issue, if I do not solve anisotropic Eliashberg equation to get Tc, but rather simply use McMillian's equation to estimate Tc (with lambda and omega_log calculated from 'a2f'), is that justified for a superconductor with no inversion symmetry? In McMillian's equation, "lambda" is an average electron-phonon coupling assuming the system is isotropic. Is my understanding correct?
Thank you again for your help.

Dr. Hanghui Chen

Hi,

McMillan equation has derived based on solutions to ME equations (you can look at the original paper by McMillan).

If the system is isotropic, McMillan equation should give very close results for Tc as the ones found by solving the isotropic ME equations. Solving the isotropic ME is very cheap and you only need a2F, but in addition you can get information about the magnitude of the superconducting gap.

If the system is anisotropic, then you need to solve the anisotropic ME equations.

Best,
Roxana

Dear Roxana,
Thank you very much indeed. Your answer is helpful.

Dr. Hanghui Chen