Spatially–resolved analysis of edge–channel equilibration in quantum Hall circuits

We demonstrate an innovative quantum Hall circuit with variable geometry employing the moveable electrostatic potential induced by a biased atomic force microscope tip. We exploit this additional degree of freedom to identify the microscopic mechanisms that allow two co–propagating edge channels to equilibrate their charge imbalance. Experimental results are compared with tight–binding simulations based on a realistic model for the disorder potential. This work provides also an experimental realization of a beam mixer between co–propagating edge channels, a still elusive building block of a recently proposed new class of quantum interferometers.