[Pw_forum] electron-phonon coefficient
azgre at azgre.com
Sun Apr 12 23:06:26 CEST 2009
Well, there are several ways to skin the cat.
1. The most correct way is to calculate "aph2F(w)". How you do this: you
have to numerically get double integral over the calculated Fermi
surface for the function <k|M(k,k')|k'>*ds*ds'. You will need partial
<k,etha| for each point at FS, where etha is relativistic quantum
number. Many years ago I have written the code for RAPW wave functions
basis. Took me 2 years to write matrix element and code for transition
metals, and to get it working. But computers were slow then, and it was
RAPW (non-linearized!). RLMTO and LAPW were not born yet. Phonon
frequency appears through |k-k'|=q in the matrix element.
2. If you don't have heavy metals in your system, you can get away
without relativistic effects. It will make your life easier, but you
still need double integral over the real FS, and real phonon spectra.
General ideas may be found in Ziman's "Electrons and Phonons". Oldest
3. If you don't have substantial p-, f- and d-electron state density at
Ef, (s-electrons->spherical FS), you can use pseudopotential matrix
element, and double integral converts into single integral over dq3 for
expanded zone. You can pull it out using tetrahedron, or whatever BZ
integration method. Much easier, I think it is in Ziman too.
4. You may voluntary ignore the fact that "alpha2" really depends on
omega. It does, but most people don't even think about writing so
involved code. The matter is decided by balance of time at hand,
ambition, braveness and laziness of specific individual. Anyway, if you
believe that your "alpha2" is practically constant, you can use
Hopfield-McMillan approach. It lets you to derive lambda and
lambda(k,k'), but there is some risk (at very extreme this may cost you
20-25% error for lambda). All you will need in this case will be partial
state densities at Ef. You simply circumvent all phonon dependence of
"apha2", and bravely use <w> and <w2>.
5. Finally, if you are extremely lucky, you may find experimental tunnel
spectra or point-contact spectra for your compound. But it is really a
Now, where to read more. First of all, look at Ziman. Going beyond that
: it is not a self-promotion, it is just easier for me to do it this
way. Go to http://www.azgre.com/PERSONAL/zhtpersonal.htm, and from the
list of publications look at 4., 8., 9., 13., 14., 57, and 59 (this one
is hard to find, it's on "pseudizm" in EPI). Look at references in these
Good luck, and please don't hesitate to ask more questions.
> Dear PWSCF users,
> 1. I want to calculate the electron-phonon coefficient "lamda" and the
> function "square of alpha" F(w) plot, how i do?
> 2. I also want to calculate IR spectra and Raman spectra?
> Thanks in advance!!
> Kind Regards
> Sanjeev Gupta
> S. K. Gupta
> PhD Candidate,
> Dept. of Physics,
> Bhavnagar University.
> Bhavnagar, 364 002., Gujarat.
> Pw_forum mailing list
> Pw_forum at pwscf.org
-------------- next part --------------
An HTML attachment was scrubbed...
More information about the users