# Implemetation of NEGF in TranSIESTA

I have a general query regarding NEGF approach:

In TranSIESTA code, when self-energy of the electrodes is calculated, does it require the coupling elements of the electrode with the central scattering region? Or,does it require just the interaction between the principle layers of the leads?

• You can get your second question back by clicking on my edit. Please ask each question in a separate post. Aug 20, 2023 at 10:11
• okay @NikeDattani Aug 20, 2023 at 10:14

Self-energies are calculated from a pristine, bulk calculation of only the electrode.

This is a requirement of the self-energy algorithm. This also forces the boundary conditions of the electrodes.

Since, the calculation is: $$\mathbf G^{-1} = \begin{bmatrix} \mathbf S_1 e - \mathbf H_1 - \Sigma_1 & \cdots \\ \vdots \\ \end{bmatrix}$$ The $$\Sigma_1$$ is the self-energy which is derived from the bulk electrode named $$1$$. However, the above requires that the electrode in the device region is equivalent to the bulk electrode region.

The initiated reader will notice that one can choose $$\mathbf H_1$$ between two values:

• the pristine bulk Hamiltonian: TS.Elec.<>.Bulk true
forces the coupled region in the device region to be very electrode bulk like
• the device region Hamiltonion: TS.Elec.<>.Bulk false
forces the electrode part of the device to couple to a bulk electrode with bulk properties. This can in some cases spare you some layers of electrode in the device region.

It is always the user's responsibility to ensure the boundary conditions are fulfilled! TranSIESTA will/can not check this.

• I have one more query. While calculating the retarded Greens function, does it chose the hamiltonian for the complete L-C-R region (see PHYSICAL REVIEW B, VOLUME 65, 165401) or the central region (see Computer Physics Communications 212 (2017) 8–24)? Maybe, I am confused here. Aug 21, 2023 at 6:52
• @sushil check out the updated answer Aug 21, 2023 at 8:54
• I was asking about the retarded Green function which is involved in the electronic transmission function $\tau_{el}(\epsilon)$. That green function should include the central region hamiltonian or of additional leads also. As, in Eq. (1) of your paperComputer Physics Communications 212 (2017) 8–24), i.e, ${\bf G}(z) = [z{\bf S} - {\bf H} - \sum_{i}\Sigma_i(Z)]^{-1}$. Which ${\bf H}$ is used here? Aug 21, 2023 at 9:12
• I don't know what you mean? You can't calculate the transmission of a device without the central region Hamiltonian. The only ambiguity there is, is about the electrode region Hamiltonian elements, as mentioned above? Aug 21, 2023 at 10:18
• The same goes for the retarded Green function... Aug 21, 2023 at 11:58