# Surface Greens' function in coherent transport calculations

1. Jul 11, 2008

Hi,

I've been reading these forums for quite a while and now it seems like a good moment for my first post. I'm doing simple coherent transport calculations in tight-binding approximation. The device Hamiltonian matrix $$H_D$$ is connected to two ideal leads, characterized by the unit cell lead Hamiltonian $$H_0$$. Let the intercell Hamiltonian be called e.g. $$V$$: this connects the lead unit cells to each other and the leads to the device.

The problem is simple: how do I calculate the surface Green's functions needed for the self-energy? I've been reading the books by Datta and Ferry, but the finite-difference methods described there don't seem to be applicable to my case. The material in my mind is graphene, but the problem should be quite general. Could someone e.g. explain in some detail how the recursive Green's function technique (RGF) actually works in my case?

I've been reading also numerous articles, but none of the methods seems to work as simply as I wish :)

I would also appreciate very much references and discussion of different methods to calculate the self-energies.

Thank you so much for any help!

2. Jul 11, 2008

As usual, right after writing this post I found a method that seems to work quite well. The problems I had were probably related to the singularities in the surface Green's function, and they could be avoided by calculating the self-energy directly. The method I used is based on solving the quadratic eigenvalue problem for lead modes, and it remains to be seen how this works after introducing e.g. the magnetic field.

Anyway, I'd still very much appreciate any discussion on the subject :)

3. Apr 1, 2009

### sokrates

Datta's approach is still valid in your case. In fact what you describe is the Non-Equilibrium Green's Function Formalism he has developed in his book. I don't think there's any other textbook that treats the matter like him (including the contacts, per se)

There are a number of ways to calculate the self-energies. One way is to use the recursive method (as explained in QTAT). Or you could solve the quadratic eigenvalue problem as you said.

The formalism is quite general and inclusion of the magnetic field simply introduces Zeeman splitting in the Hamiltonian if you are not dealing with spin-orbit interaction and working in the non-relativistic limit.

Thanks,

4. Dec 17, 2009

### mohsen2002

Hi
I had your problem with surface green function, surface green's function calculation is the important part o coherent calculation
There is some old method, there is a new method which is simple and effective
see 'closed-form solutions to surface green's functions';'PHYSICAL REVIEW B vol55 5266'
best wishes

5. Dec 17, 2009

### mohsen2002

Hi
I had your problem with surface green function, surface green's function calculation is the important part o coherent calculation
There is some old method, there is a new method which is simple and effective
see 'closed-form solutions to surface green's functions';'PHYSICAL REVIEW B vol55 5266'
best wishes

6. Dec 17, 2009

### sokrates

Noe that this is a very old thread.

7. Dec 17, 2009

### mohsen2002

Hi
OLD?
I said it is new, I meant it is newer than other method(like decimiation)
Ok

8. Dec 17, 2009

### sokrates

I said:

You are replying to a very OLD THREAD nobody is actively participating in.

I will check the paper you posted,

Thanks

9. Dec 17, 2009

### mohsen2002

I am sorry
My English is poor