This example illustrates how to calculate electron-phonon interaction coefficients for a (4×4×4) Monkhorst-Pack (MP) grid of q-points in fcc Al.

IMPORTANTNOTICE:

The calculation of electron-phonon coefficients is tricky. Do not attempt it unless you have a clear idea of the technical problems (e.g. very slow convergence with k-point grid, divergence at q=>0 for optical modes). Carefully read the relevant literature first.

The calculation proceeds as follows (for the meaning of the cited input variables see the appropriate INPUT_* file)

1) make a self-consistent calculation for Al using a dense grid of k-points.

The dense grid must contain all k and k+q grid points used in the subsequent electron-phonon calculation and must be dense enough to produce accurate el-phon coefficients (in particular the double-delta integral at E_f is very critical). Note that you have to use unshifted grids (k1=k2=k3=0) only, that include k=0! This example uses a (16×16×16) MP grid. Note that the k-point grids used here are NOT dense enough for a serious calculation!!! The option "la²F=.true." instructs the code to save data into a "a²Fsave" file, subsequently read during the el-phon calculation (input=al.scf.fit.in, output=al.scf.fit.out)

2) make a self-consistent calculation for Al using a grid of k-points that is suitable for good self-consistency and phonon calculation.

This example uses a (8×8×8) MP grid. (input=al.scf.in, output=al.scf.out)

3) make the phonon and electron-phonon calculation for the grid of q-points.

Specify elph=.true., and the name of a file where the derivative of the potential isstored "fildvscf". This example uses a (4×4×4) MP grid of q-points (nq1=4, nq2=4, nq3=4). The output contains the results for the el-ph coefficient at each q-point lambda(q), gamma(q), and the double-delta integral at several values of the gaussian broadening (set in file PH/elphon.f90). These are useful for convergence testing. (input=al.elph.in, output=al.elph.out) The results are also written into output files "a2Fq2r.*", one per value of the gaussian broadening, for further use.

4) Bring to r-space both force constants and el-phon coefficients using "q2r.x".

Output in files "a2Fmatdyn.*", one per value of the gaussian broadening

5) Calculate gamma on selected lines using "matdyn.x" (dos=.false.) .

6) Calculate lambda coefficient (in file "lambda") and the a²F(omega) function using "matdyn.x" (dos=.true.).

7) Calculate lambda coefficient (in "lambda.out") and T_c using "lambda.x".