transmission pathways, electron or current?

[sunray55]

From the video on homepage of quantumwise website, it says that "the arrow of transmission pathways inself obviously designates the direction of the electron flow". However, in the update-ATK11.2.pdf, it says "These can then be plotted as arrows, which gives a very pictorial representation of how the current flows"
As we know the current flow direction is the opposite direction of electron flow direction. Therefore, one of them must be wrong.
In my opinion, the arrows indicate the current flow since the arrow direction is from high voltage electrode to low voltage electrode if a small bias is applied (Note that it is not zero bias in all tutorials about transmission pathways).  Any physical explanation on this? Thanks.

[Anders Blom]

Although these statements are not meant to serve as documentation for the direction of the arrows, but rather in general make a statement of what the arrows mean pictorially, you are of course completely correct. I'm sorry for the confusion, we have used the terms "current" and "electron flow" interchangeably in this context, which is sloppy.

We will update the documentation in the reference manual to clearly point out how the direction of the arrows is related to the current.

[sunray55]

Thanks for your confirmation of my guess.
May I have one more question?
Based on band structures, the edged state of H-terminated GNR is flat pi near the Fermi level. The C-C sp2-sigma is far away from the Fermi level. (Son et al. PRL 97, 216803 (2006)) Therefore, the electron transport should be at the edged pi bonds. The calculated transmission pathways of H-terminated GNR (http://quantumwise.com/forum/index.php?topic=1068.msg5305#msg5305) prove the current flows along the edge. However, it shows the current mainly flows between C-C pair without bond and partially flows between C-C sp2-sigma bonds. How to explain the transmission pathway is not along the pi bonds? Thx

[Anders Blom]

The picture is intended as a nice illustration rather than to show a particular results for this system. It's computed rather crudely, and not even self-consistently.

That said, I have seen, in a recent conference presentation, similar pictures where also the current is directed not along the nearest neighbor bonds, so maybe there is something to it. It would be useful to study the corresponding transmission eigenstate, it would probably show the type of bonding character involved.