[Pw_forum] a question about electron-phonon coupling

[Malgorzata Wierzbowska]

On Fri, 29 Sep 2006, li quan wrote:

> Dear all,
>   I'm doing the electron-phonon coupling calculation. I find that in the
> source file *elphon.f90* it writes as follows:
>
>
> *parameter (eps = 20.d0/13.6058d0/8065.5d0)*
> *........*
> *.......*
> *.......*
> *if (sqrt(abs(w2(nu)) .gt. eps ) then*
> *    lambda = gamma/3.1415926/w2(nu)/dosef*
> *else*
> *    lambda = 0.0*
> *.......*
> *.......*
> **
> So I want to know why it sets *eps=20,* can we change the value of *eps?


  This is only for writing "an approximate" lambda_q, for given q-phonon,
to the output file which concerns everything for the one "recently calculated"
phonon vector. The epsilon has an arbitrarily small value to avoid 
contribution from phonons with small frequencies.

The problem with small frequency phonons comes from the fact that the 
phonon linewidths (gamma) may decrease with frequency slower than
the frequency itself. And the contribution of such phonons blows
the el-ph to infinity. This is a numerical problem correlated with
the problem of nonzero phonons (and phonon linewidths) at the Gamma point.

The remedy to this problem is to impose the accustic sum rule (which says
that phonons, and the phonon linewidths at the Gamma point are zero).
The sum rule is programmed in the part of the espresso package
where we sum over the q-phonons
(this is in pwtools in q2r and matdy;
zasr='simple' if you look at example07).

So after summation of all phonons, the el-ph comes without any
"approximation" with epsilon you mentioned.

Unfortunately nobody so far succeded to obtain good results for
the phonon vectors q which are very close to the Gamma point
without imposing anything "ad hoc".

Actually the part of elphon.f90 with the epsilon which you mentioned is 
written by Francesco Mauri and probably he could give you a better
explanation of the use of 20Ry as a cutoff.

     Gosia