Quantized two terminal conductance, edge states and current patterns in an open geometry 2-dimensional Chern insulator

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 single channel leads and the sample. We examine this assumption in a microscopic model of a Chern insulator connected to leads, using the nonequilibrium Green's 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 single channel with perfect contact is emergent, thus justifying the LB theory. The quantized two-terminal conductance shows interesting finite-size effects and dependence on system-reservoir coupling.