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tfrederiksen / inelastica

Python package for eigenchannels, vibrations and inelastic electron transport based on SIESTA/TranSIESTA DFT
https://tfrederiksen.github.io/inelastica
GNU Lesser General Public License v3.0
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local heating in Inelastica #49

Closed zhikai-zhao closed 5 years ago

zhikai-zhao commented 5 years ago

dear developments and users

I used Inelastica, the python tool of siesta/transiesta, to calculate local heating in molecular junction. After running Inelastica, there are some information about heating for a certain phonon mode, such as " heating 2.934396e+10 (1/(sV))".

My question is what the value and the unit mean? For a bias voltage, for example 0.5V, what is the power of this phonon mode that transfers the energy into heat?

thanks in advance.

tfrederiksen commented 5 years ago

The key quantity being reported here is MM.trace(MM.mm(M, GF1.AL, M, GF2.AR)). In the LOE approach this expresses the rate of phonon emission per unit of applied bias voltage. Please see Eqs. (49)-(50) in PRB 75, 205413 (2007).

In your example at V=0.5V the emission rate would thus be ~ 15 phonons/ns.

zhikai-zhao commented 5 years ago

Frederiksen, thanks for your reply. I have another question, can the rate of phonon absorption be calculated by Inelastica?

tfrederiksen commented 5 years ago

Hi @zhikai-zhao, phonon absorption is related to the electron-hole pair damping rate which, in the LOE, is expressed in terms of the factor MM.trace(MM.mm(M, GF1.A, M, GF2.A)). See Eq. (48) in the paper mentioned above. This quantity is also in the output files.

zhikai-zhao commented 5 years ago

Hi Frederiksen, in the output files, the unit of e-h damping is (1/s), should e-h damping be bias-independent? For example, 3.0e10 (1/s) means that the absorption rate is about ~30 phonons/ns. Is that right?

Thanks so much

tfrederiksen commented 5 years ago

In principle both the emission rate and e-h damping are bias-dependent (involving an integral over energy), but in the LOE approach this is simplified by evaluating the rates at the voltage threshold for phonon emission, that is V=\hbar\omega_i (or simply V=0 in the original LOE-WBA).