  The quantization of the two terminal conductance in 2D topological systems is
justified by the Landauer-Buttiker (LB) theory that assumes perfect point
contacts between the leads and the sample. We examine this assumption in a
microscopic model of a Chern insulator connected to leads, using the
nonequilibrium Greens function formalism. We find that the currents are
localized both in the leads and in the insulator and enter and exit the
insulator only near the corners. The contact details do not matter and a
perfect point contact is emergent, thus justifying the LB theory. The quantized
two-terminal conductance shows interesting finite-size effects and dependence
on system-reservoir coupling.
