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<H2><A ID="SECTION00053000000000000000">
4.3 Calculation of electron-phonon interaction coefficients</A>
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<P>
Since v.5.0, there are two ways of calculating electron-phonon
coefficients, distinguished according to the value of variable
<TT>electron_phonon</TT>. The following holds for the case
<TT>electron_phonon=</TT> <TT>'interpolated'</TT> (see also Example 03).
<P>
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 <B>k</B>-point grid to calculate phonons on a suitable
wavevector grid;
a dense <B>k</B>-point grid to calculate the sum at the Fermi energy.
The calculation
proceeds in this way:
<OL>
<LI>a scf calculation for the dense <IMG STYLE="height: 1.63ex; vertical-align: -0.10ex; " SRC="img3.png"
ALT="$\bf k$">-point grid (or a scf calculation
followed by a non-scf one on the dense <IMG STYLE="height: 1.63ex; vertical-align: -0.10ex; " SRC="img3.png"
ALT="$\bf k$">-point grid); specify
option <TT>la2f=.true.</TT> to <TT>pw.x</TT> in order to save a file with
the eigenvalues on the dense <B>k</B>-point grid. The latter MUST contain
all <IMG STYLE="height: 1.63ex; vertical-align: -0.10ex; " SRC="img3.png"
ALT="$\bf k$"> and <!-- MATH
${\bf k}+{\bf q}$
-->
<IMG STYLE="height: 1.63ex; vertical-align: -0.10ex; " SRC="img3.png"
ALT="$\bf k$"> + <IMG STYLE="height: 1.52ex; vertical-align: -0.55ex; " SRC="img1.png"
ALT="$\bf q$"> grid points used in the subsequent
electron-phonon
calculation. All grids MUST be unshifted, i.e. include <IMG STYLE="height: 1.63ex; vertical-align: -0.10ex; " SRC="img3.png"
ALT="$\bf k$"> = 0.
</LI>
<LI>a normal scf + phonon dispersion calculation on the coarse <B>k</B>-point
grid, specifying option <TT>electron_phonon='interpolated'</TT>, and
the file name where
the self-consistent first-order variation of the potential is to be
stored: variable <TT>fildvscf</TT>).
The electron-phonon coefficients are calculated using several
values of Gaussian broadening (see <TT>PHonon/PH/elphon.f90</TT>)
because this quickly
shows whether results are converged or not with respect to the
<B>k</B>-point grid and Gaussian broadening.
</LI>
<LI>Finally, you can use <TT>matdyn.x</TT> and <TT>lambda.x</TT>
(input documentation in the header of <TT>PHonon/PH/lambda.f90</TT>)
to get the <!-- MATH
$\alpha^2F(\omega)$
-->
<I>α</I><SUP>2</SUP><I>F</I>(<I>ω</I>) function, the electron-phonon coefficient
<I>λ</I>, and an estimate of the critical temperature <I>T</I><SUB>c</SUB>.
</LI>
</OL>
<P>
See the appendix for the relevant formulae.
<B>Important notice</B>: the <!-- MATH
$q\rightarrow 0$
-->
<I>q</I>→ 0 limit of the contribution
to the electron-phonon coefficient diverges for optical modes! please
be very careful, consult the relevant literature.
<P>
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