Dear sergey,
In what I explain here, I assume that your system is 1D but the method can be applied to higher dimensions (with more complications).
There is two situations corresponding to you problem: the first, is that your leads are constituted with the same repeated region as in your central system (in this way ,the whole system is periodic).
The solution,is to perform a decimation procedure, which consists of taking off a part of the system and replacing it by the proper greens function. this procedure is applied for all the cells (repeated region). in other words:
let us suppose that the length of your region (cell ) which is repeated is L
So we have the onsite potential verifies
V_{i}=V_{i+n L} for each n, and i .
*we take off, in each cell, the sites from 1 to L-1 ( so, in the whole system, only the sites of index L remain in each cell)
* the sites V_{nL} will be renormalized , and get the new potential V_{nL}+g_{11}+g_{L-1,L-1}
where g_{11}, g_{L-1,L-1} are the `Surface `greens function elements of the region of length L-1, when not attached.
*the hopping between the remaining sites (V_{nL}) is g_{1,L-1}
Now, you obtain a uniform system with renormalized hoppings and onsite potentials whose green function G is straightforward
G_{0,nL}= Exp[I N theta] /(2 g_{1,L-1} Sin[theta])
with theta defined as,
Cos[theta]= (E-(V_{L}+g_{1,1}+g_{L-1,L-1}))/(2 g_{1,L-1})
To use the Landauer Buttiker formula, you need Gamma,
Gamma=Sqrt{ 4 g_{1,L-1}^2 -(V_{L}+g_{1,1}+g_{L-1,L-1})^2}
Some remarks:
your conduction band is no more [-2,2]. the new conduction band is defined by the energies for which Gamma exists (the element inside square root is positive).
You can verify, Analytically (straightforward calculations) that T(E)= Gamma G Gamma G^* =1 in all the band .
I repeat that the band is no more (-2,2), but , in general, it will be a union of small intervals, so the profile of you transmission will be a sequence of 0 and 1 (1 inside the conducting band)
So, the problem in this case is trivial.
The second situation is when your leads are different from the central system.
in this case, you can use the exactly the same method, and arrive to a uniform system connected to two different leads. then you can use the Green propagator of a finite chain
g_{1,n}= -Sin[theta]/Sin[(n+1) theta] ( be careful, i did not put the renormalized sites here)
At the end you can arrive to a system of two sites connected to two leads. the conductance can be obtained analytically.
(in this case, the conductance will not be 1 in all the conduction band).
So, in the two cases, the result can be obtained analytically (up to the obtaining of the greens function elements of the repeated region).
check the attached file for more clarification.
I hope that this helps you
best regards
Adel