Evaluating Source Matrix in an open system
Hi
Would you plz look at the following NEGF eqn for an open system ?
(EIHsigma)*psi=S=tau*phi;
or, psi=G*tau*phi;
Here psi is device wavefunction and phi is source wavefunction.
if the system is a long semi infinite 1 D unit cell chain of same potential+effectv mass, can I tell that the wavefunction is also same everywhere?
The reason of why I think so is:
since greens function of every cell in this infinite chain is same (thats why we can recursively solve greens function for contact), and every cell sees the same infinite source to its rightside, each of the cell should have same psi.
Now if I go to evaluate psi of the first cell, I get, from Schrdngr eqn:
psi=G*tau*psi
(looks somewhat similar to the equation: G = inv( EIHtau*G*tau' );
However, the above equation for psi is a bit unusual, since it says, the matrix (G*tau) should have a eigenvalue =1, and the corresponding eignvector will be psi. It means, for a given energy, I have to calculate G first, and then see if (G*tau) has any eigenvalue =1. If not, there will be no psi for that Energy.
Isn't it weird? Should it happen for a open system? Am I making wrong idea somewhere? Am I overlooking any phenomenon, such as scattering from leftside coupling for a unit cell?
Actually I need to evaluate the column vector 'S' in Schrodingr eqn for a given energy (S=tau*phi). Please refer me to any formalism of evaluating S.
Thank you.
