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

The quantization of the two terminal conductance in 2D topological systems has been observed in experiments and is usually justified by the Landauer-Buttiker (LB) theory supplemented with two additional assumptions namely single channel leads and perfect point contacts between the leads and the edge states. We examine these assumptions in a microscopic model of a Chern insulator connected to leads, using the nonequilibrium Green's function formalism, and provide numerical evidence to justify them. Our numerics shows perfect quantization of the two terminal conductance. Remarkably, we find that the charge currents exhibit highly localized patterns in the leads, 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.