Transmission Eigenstates - linear combination of the Bloch states

[89aj]

Dear QW and users,

I'm trying to identify and separate transmission eigenstates by similarity across energy and k-points. My issue is that if I have two eigenstates that contribute almost equally - in fact it changes across energy and k-points which one that contribute the most - I can't use the quantum number to identify them.

I was thinking that if I could get the e_a,n (the linear combination of Bloch states, http://docs.quantumwise.com/manuals/Types/TransmissionEigenstate/TransmissionEigenstate.html) then I could do the cross-product of the e_a,n vectors and similar eigenstates would be small compared to very different eigenstates.

So is it possible to get e_a,n?

I've tried the toArray method, but it is too heavy to save all eigenstates on a grid across many energies and k-points for such a comparison to be practical.

Maybe there is another way?

Thank you,
Anders

[Daniele Stradi]

Hi,

If I understood the question correctly, I do not think that what you propose is possible, because the transmission eigenchannels do not have the same symmetry as the Bloch states, see PRB 76 115117 (2007).

However, you can still calculate the transmission eigenstates for different energies and k-points, and then compare them directly.

Regards,
Daniele.

[89aj]

Thanks Daniele.

Can you explain what you mean by comparing them directly?

[Jess Wellendorff]

You may plot them in 3D: https://docs.quantumwise.com/tutorials/atk_transport_calculations/atk_transport_calculations.html#transmission-eigenstates

[Kim_W]

How to set k-point (ka and kb) in transmission eigenstates?

[Petr Khomyakov]

This can be done in the Calculator settings, see https://docs.quantumwise.com/tutorials/atk_transport_calculations/atk_transport_calculations.html.

[Kim_W]

There are three transmission values. How to choose it?

[Petr Khomyakov]

What do you mean by "How to choose it?"? For a given energy and k-point, there may exist several transmission channels, e.g., 3 like in your case. The graph for T(E) shows you the total transmission, which is the one of relevance for the actual conductance/current calculations.