Dear Anna, Thanks for the interest. I just want to point out that this mailing list should be to Kwant related questions, not purely physics questions. Altough, of course physics questions will arise in this context.
For purely physics questions you may try https://physics.stackexchange.com/, for example. I answer below your questions. 1 - My apologies! I forgot to mention the change! I just saw it and changed it, because I assumed that you wanted to simulate a Chern insulator. Now I have read more carefully that you want Zeeman and Rashba spin-orbit interaction, following the Kwant tutorial. 2 - This system (Zeeman + Rashba) is not fully gapped, there is a spin-orbit gap that means an avoided crossing between the different spin bands, but there is no spectral gap. Therefore, the Hall conductivity (sigma_xy) is not quantized. The 2 or 4 terminal conductance may differ from the sigma_xx, sigma_xy Kubo conductivtiy, depending on the transport setup, geometry, etc. The two terminal conductance (with perfectly metallic leads) should give you the sum of steps of value 1 for each band that has modes at the specific energy. This should be reproduced by the Kubo sigma_xx conductivity (or sigma_yy, it may differ). To simulate the Hall conductivity you need a 4 terminal setup (see Ref [1]), and this should be reproduced by the Kubo sigma_xy conductivtiy. 3 - I imagine that with pen and paper you derive the Bloch Hamiltonian of the system that depends on k_x, k_y. This means that you have the bandstructure for a 2D plane, and this bands from a set of surfaces in 3D, if you plot the energy along the z axis. In a system with 1D translational symmetry (a Kwant lead) you have many modes, depending on the with of the lead, transverse to the propagation direction. The bands of the lead are (more or less) like perpendicular cuts of the 3D dispersion relation of the bulk 2D system, but projected along the k-direction of the lead. See [2] for graphene nanoribbons, or the Kwant tutorial 2.4. I hope this helps, and points you to the right sources to fill-in the gaps. Best, Pablo [1] Four-Terminal Phase-Coherent Conductance. M. Büttiker Phys. Rev. Lett. 57, 1761 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.57.1761 [2] https://en.wikipedia.org/wiki/Graphene_nanoribbon
