[Pw_forum] electron-phonon coefficient

AZGlobal 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 
but goldest.
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.
Dr. A.Zhako-Titarenko
> 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.
> <http://sigads.rediff.com/RealMedia/ads/click_nx.ads/www.rediffmail.com/signatureline.htm@Middle?> 
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