Surface Greens' function in coherent transport calculations

[saaskis]

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!

[saaskis]

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 :)