how to get the table?

[yangzw1985]

Hellow, everyone! I have been puzzling about the table 2 in Nano Lett. 2008 Nov;8(11):3662-7. Epub 2008 Oct 14.

I do not understand what is the real meaning of the first three Eigenchannels of the transmission? I want to know how to obtain the channel 1, channel 2 , channel 3 ,and the others?

In order to understand the table, I have try to calculate the transmission eigenstates and transmission eigenvalues of my two probe model, but the results are not like this.

In table 2, they also calculate the percentage probability of transmission, in my opinion, one channel should have a value, the wire should have lots of channels, so we can calculate the percentage. I don't know what I have said is right or not?

Can anyone tell me  how to distinguish the channel 1, channel 2 and channel 3.......? In other words, if I want to obtain the table, what should I do?

Thanks in advance!

[nori]

Dear yangzw1985,

>In order to understand the table, I have try to calculate the transmission eigenstates and
>transmission eigenvalues of my two probe model,

You're right.
"Eigenchannel" in the paper is equivalent to "transmission eigenstates" in ATK.
Also, the value of channel X in the table 2 is equivalent to "transmission eigenvalue" in ATK.
For instance, the coefficient of 1st channel of <100> at Fermi energy is 0.01*0.76= 0.0076.


>but the results are not like this.

What do you mean about it?
Have you tried to calculate completely the same system as one in the paper ?
Or have you done similar calculation but not for the same system in the paper?


>In table 2, they also calculate the percentage probability of transmission, in my opinion, one channel should have a value,
>the wire should have lots of channels, so we can calculate the percentage. I don't know what I have said is right or not?

You're right.
Maybe more correctly, the 2probe system has several transmission channels at each energies,
so we can calculate the percentage of each channels against total transmission(= sum of transmission eigenvalue) at some energy.


>Can anyone tell me  how to distinguish the channel 1, channel 2 and channel 3.......?
>In other words, if I want to obtain the table, what should I do?

You should do the calculation of transmission eigenvalues at Fermi energy.
http://www.quantumwise.com/documents/manuals/ATK-2008.10/ref.calculatetransmissioneigenvalues.html

[yangzw1985]

Thank you for your valuable and clear reply, Nori ! I will try again to calculate the transmission eigenvalues.

[yangzw1985]

Hi,everyone! I have calculated the transmission eigenvalues of my two probe model. Attached is the results.To be honest, I do not understand the results. Can anyone tell me what is the real meaning of the results?

Moreover, fig 3 and fig 5 in physical review B 71,165316(2005) have plot the MPSH eigenvalues are marked with circles for DTB and with triangles for OPV3. I want to know if I calculated results is equal to the MPSH eigenvalues. However, the results are not like the value in FIG 3 and FIG 5. Plese tell me the differents of the results? And how to got the MPSH eigenvalues  in fig 3 and fig 5?

Thanks in advance!

[Anders Blom]

You have mixed up completely different concepts here, I'm afraid

THE MPSH eigenvalues, as used in the reference you mention, show how the molecular levels are affected by the coupling to the electrodes. MPSH = molecular projected self-consistent Hamiltonian. By diagonalizing this projected Hamiltonian, and comparing the eigenvalues to the isolated molecule, you can see how the levels are shifted due to the influence of the electrodes. Often, it's the change of the HOMO-LUMO gap which is of interest.

The transmission eigenvalues show how the transmission spectrum is broken down into components. For a particular energy E, there may be several channels contributing to the transmission, and by computing the transmission eigenvalues you see how many. Each transmission eigenvalue must be <=1 but the total transmission T(E) can be > 1 if you add up the channels.

In your case, the transmission eigenvalues are all zero, meaning the transmission itself at this energy is also zero.

[yangzw1985]

Hi, Ander Blom! I know MPSH = molecular projected self-consistent Hamiltonian. Can you tell me, in FIG 3 and FIG 5, If the value of circles and triangles are represent the value of projected Hamiltonian energy spectrum of two probe model.

I also calculate the projected Hamiltonian energy spectrum of my two probe model. From the calculated results, the homo - lumo gap is 0.18. As can we see from the energy spectrum, there are lots of values,and some of the values are equivalent. I also do not know the reason.

Now that there are so many values, if I want to plot the value, which one should be given, just as in FIG 3 and FIG 5?

(attached file is the calculated projected Hamiltonian energy spectrum)

Thanks!

[Anders Blom]

Yes, the marks in Figs. 3 and 5 are the MPSH eigenvalues. However, to get the correct spectrum you must project the Hamiltonian onto the molecule atoms only; from the number of eigenvalues, I believe in your case you have not selected any projection atoms.

Also, I wouldn't expect to get the same results as in that paper, since your electrodes are Li, while the paper used Au.

[yangzw1985]

Thank you !

 To get the correct spectrum you must project the Hamiltonian onto the molecule atoms only;

When I perform the calculation, I just include the molecule atoms.

What is the real meaning of "Project the Hamiltonian onto the molecule atoms only"? Do I have to select the projection atoms manully? If yes, please tell me how to perform the calculation in detail.

http://quantumwise.com/documents/manuals/ATK-2008.10/chap.advtwoprobe.html#sect1.advtwoprobe.dos

I also have read the tutorial  of the spectrum caculation of li-h2-li system. In this tutorial, scf, projection_atoms = [3,4].

If I want to obtain the right spectrum, how to select the projection atoms. Does it should be include all of atoms of  the C nanowire?

I have tried to select the atoms in the follow script.  Please have a look at it, and tell me is right or not.
The Li atoms of  left or right  electrodes is 64. In the central region, the Li atoms is 96. And the C wire atoms is 307.

I want to Know if the calculation should include the Li atoms in the central region.

Thanks again for your reply!

[Anders Blom]

The MPSH concept as such does not really apply to the kind of system you have, since there is no well-defined "molecule" for which you can compute the spectrum in the absence of the electrodes, to compare to the MPSH spectrum (molecule with electrodes).

[yangzw1985]

Do you meaning I can not calculate the MPSH spectrum for the two-probe model? In other words, we can not get the right spectrum of my two probe model. Is it right?

If I want to calculate the transmission properties of My two probe model, how to analysis the calculated  transmission spectra and I-V characteristics? In my opinion, LUMO-HOMO gap is the fundamental reason.

[Anders Blom]

You have built a very beautiful and interesting system, but the central region is not a molecule, so it makes no sense to talk about a "molecular" projected Hamiltonian or HOMO/LUMO; these are all concepts related to finite system, not nanowires.

Your nanowire is probably semiconducting, which would explain the small transmission. But at any rate, the relevant concepts are the band structure of the nanowire, and other bulk concepts.