4.3 Calculation of electron-phonon interaction coefficients

Since v.5.0, there are two ways of calculating electron-phonon coefficients, distinguished according to the value of variable electron_phonon. The following holds for the case electron_phonon= 'interpolated' (see also Example 03).

The calculation of electron-phonon coefficients in metals is made difficult by the slow convergence of the sum at the Fermi energy. It is convenient to use a coarse k-point grid to calculate phonons on a suitable wavevector grid; a dense k-point grid to calculate the sum at the Fermi energy. The calculation proceeds in this way:

1. a scf calculation for the dense $\bf k$-point grid (or a scf calculation followed by a non-scf one on the dense $\bf k$-point grid); specify option la2f=.true. to pw.x in order to save a file with the eigenvalues on the dense k-point grid. The latter MUST contain all $\bf k$ and $\bf k$ + $\bf q$ grid points used in the subsequent electron-phonon calculation. All grids MUST be unshifted, i.e. include $\bf k$ = 0.
2. a normal scf + phonon dispersion calculation on the coarse k-point grid, specifying option electron_phonon='interpolated', and the file name where the self-consistent first-order variation of the potential is to be stored: variable fildvscf). The electron-phonon coefficients are calculated using several values of Gaussian broadening (see PHonon/PH/elphon.f90) because this quickly shows whether results are converged or not with respect to the k-point grid and Gaussian broadening.
3. Finally, you can use matdyn.x and lambda.x (input documentation in the header of PHonon/PH/lambda.f90) to get the α²F(ω) function, the electron-phonon coefficient λ, and an estimate of the critical temperature T_c.

See the appendix for the relevant formulae. Important notice: the q→ 0 limit of the contribution to the electron-phonon coefficient diverges for optical modes! please be very careful, consult the relevant literature.