G.3 Surface GREEN's Function

If the potential does not vary in the left and right contacts and if the coupling between different layers are equal, then and become semi-infinite periodic matrices with

(G.23) |

Under this condition one obtains

(G.24) |

Therefore, the surface GREEN's functions can be obtained by solving the quadratic matrix equations

These equations can be solved iteratively by

where represents the iteration number. It should be noted that the solution to (G.25) is analytic if the dimension of is one.