1. In the newer versions of Kwant you must define the `norbs`, it may not be up to date everywhere in the documentation. Certainly the `kpm` module makes use of this parameter of your system.
2. The Kubo conductivity is calculated as a trace per unit cell, you can see the details in the references cited in the documentation of the `kpm.conductivity` function. For a finite system with open boudary conditions, the results will make sense if you compute this local quantity in the bulk of your system far away from the edges. To do this, you can make use of the `vector_factory` argument in the `kpm` module, for example with the `kwant.kom.LocalVectors` class.
The finite system does not need to have leads as we don't compute currents or scattering states, we compute the linear response (in some direction `x_alpha`) of the system to an electric field in some other direction (`x_beta`). These directions enter in the conductivity function with the `alpha`, and `beta` arguments.
For systems with periodic boundary conditions you need to define periodic velocity operatos and pass them to `kpm.conductivity`. This is not implemented in Kwant and can be tricky to define.
In both cases, you need to normalize the results by the area that each of your vectors cover.
By the way, I tried running your sistem and does not show a gap. Therefore, the conductivities are not quantized to a topological invariant.
Here a snippet of how you could define the local vectors in your case
``` edge_width = min(L, W) / 4
def center(s): return (edge_width <= s.pos < L - edge_width) and (edge_width <= s.pos < W - edge_width)
center_vectors = np.array(list(kwant.kpm.RandomVectors(syst, where=center))) # here kwant.kpm.LocalVectors can also be used, but will produce much more vectors num_vectors = len(center_vectors) norm = np.linalg.norm(center_vectors) ** 2
num_vectors=num_vectors, vector_factory=center_vectors ```
I hope this helps, regards, Pablo