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In the paper 'Improvements on non-equilibrium and transport Green function techniques: The next-generation transiesta and in particular in figure 10b, the I/V curve of a specific model is reported.

Naively, I would expect for the I to be 0 when the V is 0. Why in this case is different?

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1 Answer 1

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The graph in question is this:

Fig 10 in https://doi.org/10.1016/j.cpc.2016.09.022

The article describes the importance of correctly simulating the self-consistent solution for temperature gradients (not bias).

Generally, NEGF software have used the same temperature in both electrodes. But the NEGF scheme does not prohibit one from doing NEGF calculations with different temperatures + different bias.
This is the take-home message from this plot.

So what is show:

Red [square] line

This is the result of a self-consistent calculation of the electronic structure and transmission values at the shown bias points with an electronic temperature in both electrodes at $3000 K$.
Subsequently, the IV curve is calculated from the transmission values but changing the electrodes temperatures to $T_L = 3000K$ and $T_R=300K$ (i.e. non-self-consistent temperature gradient).

Blue [triangle] line

This is the result of a self-consistent calculation of the electronic structure and transmission values at the shown bias points with an electronic temperature in both electrodes at $300 K$.
Subsequently, the IV curve is calculated from the transmission values but changing the electrodes temperatures to $T_L = 3000K$ and $T_R=300K$ (i.e. non-self-consistent temperature gradient).

Black [circle] line

This is the result of a correct self-consistent calculation at the shown bias points with electronic temperatures in the electrodes as $T_L=3000K$ and $T_R=300K$.

Conclusion

The point is that there is a large difference between the 3 curves, and that one cannot simply interpolate between the curves.

The fact that there is a temperature difference between the electrodes means that a current will flow, even at 0 V.

Of course there may be many effects which will try and equilibrate such things, and phonons are not taking into account by this method. But it shows the importance of understanding the temperature effects.

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  • $\begingroup$ I understand. What I am still missing is that you say 'The fact that there is a temperature difference between the electrodes means that a current will flow, even at 0 V.' However, I understand that the red and blue line are computed which electrodes at the same T (no Temperature gradient) $\endgroup$
    – Laura
    Commented Apr 20, 2023 at 11:58
  • $\begingroup$ Could you please, carefully read the edited answer, I think you are missing the key point written? $\endgroup$
    – nickpapior
    Commented Apr 20, 2023 at 12:17
  • $\begingroup$ I think I get now the point. If I understood correctly, when you say 'electrodes with the same T', this is always in the calculation of the electronic structure whilst the I/V curve is always calculated with a T gradient. However, in the black curve case, you have a Temperature gradient through the whole calculation. Right? If this is correct, if one takes a dT=0 through the whole calculation, the I should be 0 for 0V. $\endgroup$
    – Laura
    Commented Apr 20, 2023 at 12:32
  • $\begingroup$ Yes. That is correctly understood. $\endgroup$
    – nickpapior
    Commented Apr 20, 2023 at 12:44
  • $\begingroup$ A nice and thorough answer. $\endgroup$ Commented Apr 20, 2023 at 13:14

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