how to choose the eigenchannel index

[Roc]

Dear everyone,

There is speaking in VNL mannul"Transmission eigenchannels of doped Al wire":

# Calculate the transmission eigenstates
index_list = [0,1]
kpoint_list = [(0.0,0.0)]
for index in index_list:
    transmission_eigenstate = calculateTransmissionEigenstates(
        scf,
        energy,
        quantum_numbers=(index,kpoint_list)
    )
    results.addToSample(transmission_eigenstate[0],"perfect_alwire")

I have some question about it. When I calculate the transmission eigenstates of the two-probe system, how can I choose eigenchannel index and set it in VNL

Thanks.

[serhan]

Hi anyipeng,

Quoting from the ATK manual from section "calculateTransmissionEigenstates":

"index is the transmission eigenvalue index (see calculateTransmissionEigenvalues
()). The transmission eigenvalue index may assume any integer value within the range
[0, Neigenchannels-1], where Neigenchannels indicates the number of eigenchannels which
corresponds to non-vanishing transmission eigenvalues."

So, to determine Neigenchannels, firstly you have to see the number of non-zero transmission eigenvalues.

Regards
Serhan

[Nordland]

Inside VNL you do it by dropping the twoprobe on the NanoLanguage  scripter, and selecting the analysis tab. Select the transmission eigenstates,
and the dialog below will show all the input data. In the field Eigenchannel index you simply enter the number (starting from zero) of the eigenchannel you want to calculate. Where 0 being the one with the highest transmission, and 1 then one with the second highest transmission and so on.

[Roc]

Thanks a lot!   Happy new year!

[Roc]

Dear eneryone,

The "conductance channels"  still bepuzzles me, one paper says:
"the equilibrium conductance is 5 G0, which means five conductance channels opening at the Fermi level and contributing to the total transmission."

I have calculated the ‘Transmission Eigenvalues“，the out as follows,

# -----------------------------------------------------------------------------
# Energy Spectrum
# -----------------------------------------------------------------------------
# Energy (eV)
       -21.89
       -19.75
       .........
        83.74
        84.39
        84.39
[array([  1.96681012e-01,   5.99825296e-24,  -2.78097762e-24]), array([  1.96681012e-01,   1.58750525e-24,  -7.23663503e-24])]

Is that [array([  1.96681012e-01,   5.99825296e-24,  -2.78097762e-24]), array([  1.96681012e-01,   1.58750525e-24,  -7.23663503e-24])][/b] the "Transmission Eigenvalues"

from these dates, how can I get the Transmission channels, and how to set it in the VNL like these menus as follows

Thanks!

[Nordland]

First of all - since it is a 1D system you can remove the k-points [0.5, 0.5, 0.5]. This you can do by right-clicking on it in the box 'Quantum Numbers'
You will only need [0.0, 0.0, 0.0] for your study.

The array you get printed, is the transmission eigenvalues. So in your doped wire you have 3 channels with
one with a finite transmission probability of 0.196888 and 2 that is closed ( zero probability).
So yes, it is the transmisison eigenvalues.

If the dialog box below in the field eigenchannel index if you enter the value 0. It will be the transmission eigenchannel with the highest transmission probability (0.196888), if you enter 1, it will be the transmission eigenchannel with the second highest transmission probability (5.99825296e-24), and so on...

If you want to calculate more in the same calculations, you can add "Transmission Eigenstates" multiply times.

Best regards,
 Nordland

[ipsecog]

There seems to be a small bug in VNL on this: in the widget where you specify k-points (Quantum Numbers) for "Transmission Eigenvalues", it is not possible to either add or remove k-points, so you're stuck with 2 points. You can, however, edit the points :-)

[sunray55]

First of all - since it is a 1D system you can remove the k-points [0.5, 0.5, 0.5]. This you can do by right-clicking on it in the box 'Quantum Numbers'
You will only need [0.0, 0.0, 0.0] for your study.

May I know how to set the K-points of eigenvalues in 2D system? Since the high symmtry points are [0,0,0];[0.5,0,0]; [0.5,0.5,0]; and [0,0.5,0] in 2D system, I should set four rows as [0,0]; [0.5,0]; [0.5,0.5]; [0,0.5]? Or,  I only need set [0,0] in all two-probe system (1D, 2D, and 3D).

May I know what is the difference of eigenvalues (channel) at different high symmtry points? I guess the number of channels will be the same at all high symmtry points.

Many thanks.