What is the bare phonon frequency in EPW

[zz11ss11zz]

Dear all,

According to https://docs.epw-code.org/doc/Electron- ... pling.html, the output of the electron-phonon coupling matrix |g| (by prtgkk) is g^SE.

1.png (5.96 KiB) Viewed 7912 times

The \omega_{q,\nu} in the denominator is the bare phonon frequency. Although there is no direct output of the bare phonon frequency in QE and EPW, we can obtain the bare phonon frequency by using the following formula under the double delta approximation:

2.png (2.77 KiB) Viewed 7912 times

I was wondering what I am understanding is correct or not, and how to calculate (by using which formula) the bare phonon frequency in the code?

Thank you.

Best regards,
Zishen

[hlee]

Dear Zishen:

Although there is no direct output of the bare phonon frequency in QE and EPW, we can obtain the bare phonon frequency by using the following formula under the double delta approximation:

In EPW, it comes from the previous DFPT calculations on coarse grids and then interpolated on fine grids.

Sincerely,

H. Lee

[zz11ss11zz]

Dear Dr. Lee,

Thank you for quick reply.

As I find that the bare phonon frequency \omega_{q,\nu} obtained by using the previous second formula is different from \omega_{q,\nu} obtained by cDFPT. The major difference is that the \omega_{q,\nu} (LA branch) obtained by using the previous second formula has a dip at the CDW vector (2/3GM):

3.png (8.1 KiB) Viewed 7866 times

which is similar to the bare phonon frequency shown in Fig. 5(a) of PRB 95, 235121 (2017)
However, the one obtained by the cDFPT (PRB 101, 155107 (2020)) is smooth:

4.png (22.58 KiB) Viewed 7866 times

I am confusing about such a difference.

In PRB 101, 155107 (2020), they point that such difference may be due to the neglecting of the bare phonon vertices g (eqs.2). However, the phonon self-energy is related to the difference between the bare phonon frequency and the renormalized phonon frequency (eq.2a). In other words, the bare phonon frequency is independent of the phonon self-energy?

And if the code (QE or EPW) only considers the screened electron-phonon vertices g in eq.2 [PRB 101, 155107 (2020)], the results should be self-consistent. Then the bare phonon frequency used in the code should have the dip? Thus, I was wondering about the exact definition of the bare phonon frequency in the QE (EPW), which f90 file is used to calculate the bare phonon frequency in the QE package?

Sorry about the tedious expression.

Best regards,
Zishen

[hlee]

Dear Zishen:

I think that we might say something different.

The only thing I can tell you is that when evaluating the expression (1.png) in both QE and EPW, \omega_{q,\nu} from previous (normal) DFPT calculations is used; it corresponds to the phonon frequency we normally obtain from phonon (ph.x) calculations.

Regarding the conceptual thing, other users or developers would tell you more.

Sincerely,

H. Lee

[zz11ss11zz]

Dear Dr. Lee,

It seems that the code (QE or EPW) uses renormalized phonon frequency in the calculation. It is also a very helpful answer, thanks!

Best regards,
Zishen

[hlee]

Dear Zishen:

It seems that the code (QE or EPW) uses renormalized phonon frequency in the calculation.

Yes, you are right.

After reading the paper titled "Ab initio downfolding for electron-phonon-coupled systems: Constrained density-functional perturbation theory" at http://dx.doi.org/10.1103/PhysRevB.92.245108, I confirm that the phonon code (ph.x) outputs the "fully" renormalized phonon frequencies and EPW uses them.

To my understanding, if you need to output bare ones, you need to modify the phonon code by using the expression in the paper above.

Sincerely,

H. Lee

[zz11ss11zz]

Dear Dr. Lee,

I see, thanks again!

Best regards,
Zishen