Current calculated from Inelastic transmission spectrum

[weixiang]

Dear Quantumwise experts,
I am calculating the inelastic transmission spectrum of a GNR p-n junction (see attached python file for the configuration) using the InelasticTransmissionSpectrum method in ATK.
First I calculated the Transmission spectrum and PLDOS without the e-ph interaction, which gives a current I = -8.3168 e-5 nA.  As shown  In the attached image that from the spectral current and Projected Local Density of States it can be noticed the major current contribution is from the tunneling near the Fermi level. So I am expecting the sum current (elastic+inelastic) from the InelasticTransmissionSpectrum is several magnitudes larger than that from the TransmissionSpectrum as is shown in the  case study of https://docs.quantumwise.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html
I just wonder that is it possible to get a reasonable current by just taking one or a few representative energy points in the InelasticTransmissionSpectrum method parameter setup, e.g.  0 eV or (-0.05, 0, 0.05)*eV ?
Since the spectral current at these energies is largest.
I have the InelasticTransmissionSpectrum sum current for  0 eV which is -1.38e-4 nA (one magnitude larger than the non-interacting case) and for (-0.05, 0, 0.05)*eV which is -5.84e-5 nA. (slightly smaller than the non-interacting case)
They are quite different, but which one is more accurate?  Or maybe neither?

Thank you!
Happy New Year!

[weixiang]

I think I have got the answer from the manual.
It says "If the non-interacting transmission is finite at the Fermi level (e.g. in a molecular junction with metallic leads) it will often be sufficient to calculate the inelastic transmission spectrum only at the Fermi energy and use the LOE current formula," and "In situations where there are no electrode states at the Fermi energy, like in a low- or un-doped semi-conductor, the direct use of the LOE and XLOE expressions will result in zero inelastic currents, when evaluated at the Fermi energy. In that case, the inelastic transmission spectra must be calculated at a range of energies (like the normal TransmissionSpectrum). "
So for my case I believe it is sufficient to take only the Fermi level and calculate the inelastic current.
But what if the non-interacting transmission at the Fermi level is finite but is a local minimal? (like in the attached image) In this case, is it still sufficient to take only the Fermi level for the inelastic current calculation?

In addition, I have a bit of confusion for the terminologies. I thought that the elastic current refers to the current calculated considering the elastic e-ph interaction, while the inelastic current refers to the current calculated considering the inelastic e-ph interaction.  But I learned from the manual that somehow elastic current equals to the non-interacting current. Why is this the case? But as shown in https://docs.quantumwise.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html. the elastic current is much larger than the current calculated from the normal TransmissionSpectrum which should be the non-interacting current.

[Petr Khomyakov]

I think I have got the answer from the manual.
It says "If the non-interacting transmission is finite at the Fermi level (e.g. in a molecular junction with metallic leads) it will often be sufficient to calculate the inelastic transmission spectrum only at the Fermi energy and use the LOE current formula," and "In situations where there are no electrode states at the Fermi energy, like in a low- or un-doped semi-conductor, the direct use of the LOE and XLOE expressions will result in zero inelastic currents, when evaluated at the Fermi energy. In that case, the inelastic transmission spectra must be calculated at a range of energies (like the normal TransmissionSpectrum). "
So for my case I believe it is sufficient to take only the Fermi level and calculate the inelastic current.
But what if the non-interacting transmission at the Fermi level is finite but is a local minimal? (like in the attached image) In this case, is it still sufficient to take only the Fermi level for the inelastic current calculation?

I guess it is not about having a minimum or maximum transmission at the Fermi level. The transmission is in general a complicated function of the electron energy. Verifying whether this approximation works or not (which also depends on the target accuracy you want to achieve) is something to figure out by doing the LOE vs. XLOE calculation, at least for some bias voltage(s).

Having a weak dependence of the transmission spectrum near the Fermi level suggests that  the transmission can be approximated with a energy constant within the energy window between the left and right electrode chemical potentials. In that sense, having a flat minimum suggests that the approximation might work for your system. 

In addition, I have a bit of confusion for the terminologies. I thought that the elastic current refers to the current calculated considering the elastic e-ph interaction, while the inelastic current refers to the current calculated considering the inelastic e-ph interaction.  But I learned from the manual that somehow elastic current equals to the non-interacting current. Why is this the case? But as shown in https://docs.quantumwise.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html. the elastic current is much larger than the current calculated from the normal TransmissionSpectrum which should be the non-interacting current.

Personally, I would also use a different name for this term, but this is how it is defined in the reference paper used to implement this methodology in QuantumATK. So, we stick to it for the sake of consistency. 

[weixiang]

Thank you for the reply!
So since by terminology the elastic current equals to non-interacting current then the current calculated from InelasticTransmissionSpectrum.elasticCurrent()
should be same or close to the current calculated from TransmissionSpeactrum.current()
But in this tutorial https://docs.quantumwise.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html
The TransmissionSpeactrum.current() is  -7.06766e-11 nA
while the InelasticTransmissionSpectrum.elasticCurrent() is -3.71e-09 nA
They are different by almost 2 magnitudes. I understand that they have different k-points sampling but does the k-points sampling really matter that much?

And speaking of the k-points sampling, for the quasi 1-D GNR system, in setting up the Inelastic transmission spectrum,  should I untoggle the periodicity in K_A and K_B and fix the k-points sampling as 1 in these two directions? 
And what about the q-points sampling, should I do the same thing, untoggling k_A and k_B periodicity?

[Petr Khomyakov]

They are different by almost 2 magnitudes. I understand that they have different k-points sampling but does the k-points sampling really matter that much?

The k-point sampling can matter a lot, see https://docs.quantumwise.com/tutorials/fe_mgo_fe/fe_mgo_fe.html for having an example on this issue.

And speaking of the k-points sampling, for the quasi 1-D GNR system, in setting up the Inelastic transmission spectrum,  should I untoggle the periodicity in K_A and K_B and fix the k-points sampling as 1 in these two directions? 
And what about the q-points sampling, should I do the same thing, untoggling k_A and k_B periodicity?

If you are doing calculations for a quasi-1D system, you should adopt a Gamma k-point only. Note that you should also make sure that there is a sufficient vacuum padding around the quasi-1D structure.   

[weixiang]

Thank you for the reply!
How about the q points sampling?  Should I untoggle q_A and q_B periodicity too?

Thank you!

[Petr Khomyakov]

It should use a Gamma point as well.