average phonon frequencies

[fabiocosta4]

Dear EPW community

I'm currently running some calculations with EPW 5.1, aiming to study the electron-phonon interaction in some simple systems. As part of the outputs I'm trying to determine are the average phonon frequencies <w> and the logarithmic average phonon frequencies w_log. To perform the calculations, I'm using the following setting:

Code: Select all

...
  elecselfen  = .true.
  phonselfen  = .true.
  a2f         = .true.
...

What I'm not sure is wether these logavg and l_a2f quantities are the ones I'm seeking to determine.

Code: Select all

     ===================================================================
     Eliashberg Spectral Function in the Migdal Approximation
     ===================================================================

     lambda :    0.3208895
     lambda_tr :    0.4251001
 
     Estimated Allen-Dynes Tc
 
     logavg =    0.0069899 l_a2F =    0.4189137
     mu =   0.10 Tc =         5.969107220843 K
     mu =   0.12 Tc =         3.715758994450 K
     mu =   0.14 Tc =         2.096133038087 K
     mu =   0.16 Tc =         1.035503588036 K
     mu =   0.18 Tc =         0.425181951443 K
     mu =   0.20 Tc =         0.133454674518 K
     a2F          :      0.74s CPU      0.75s WALL (       1 calls)

I read in some previous post that the logavg should be the logarithmic average phonon frequency, displayed in Ry. My next step was to try to convert it to Kelvin: logavg[K]=logavg[Ry]*157887=1103K. By entering this value into the McMillan formula, together with lambda=0.3208 and mu=0.1, it results in a crictical temperature of arround 1K, very different from the result of 5.9K.

So my main questions at this point are who are these two quantities displayed above the critical temperatures, and in which units are they being displayed.

Thanks in advance for any assistance
Fbio Costa

[roxana]

Hi Fabio,

I think you made a mistake in your estimate. This is the formula for Tc implemented in the a2f.f90 file.

tc = logavg / 1.2d0 * exp( - 1.04d0 * ( 1.d0 + l_a2F ) / ( l_a2F - mu * ( 1.d0 + 0.62d0 * l_a2F ) ))
! tc in K
!
tc = tc * ryd2ev / kelvin2eV

If I take the values

logavg = 0.0069899
l_a2F = 0.4189137
mu = 0.1
ryd2ev = 13.6056981
kelvin2eV= 8.6173427909e-05

in the equations above, I get Tc = 5.969099 K

I also converged logavg to K first, and then use the expression for Tc.

logavg = logavg / kelvin2Ry
tc = logavg / 1.2d0 * exp( - 1.04d0 * ( 1.d0 + l_a2F ) / ( l_a2F - mu * ( 1.d0 + 0.62d0 * l_a2F ) ))


In this case, I get again Tc = 5.969099 K using

logavg = 0.0069899
l_a2F = 0.4189137
mu = 0.1
kelvin2Ry = 6.333627859634130e-06

Best,
Roxana

[fabiocosta4]

Dear Roxana

Thank you for your assistance. My mistake was that I was assuming that the electron-phonon coupling constant was the value being displayed as lambda. It was unclear to me that the lambda I was looking for was the actually the l_a2f output.

Sorry for the mistake, and thak you for your assistance, it made things more clear to me now.

Cheers
Fbio