Dc Electrical Current Generated by Upstream Neutral Modes

We consider a setup made of a chiral charged edge mode and two counter-propagating neutral modes near the boundary of a quantum Hall edge. The charge mode is decoupled (tunneling-wise and interaction-wise) from the latter throught out most of the edge. These modes interact near the electrically active contact which they are tunnel coupled. We show that injecting downstream electrical current in the charge mode may result in a d.c. current measured in an upstream contact. Our conceptual setup may be realized with a simple edge mode of a quantum Hall phase, and a quasi 1-d XXZ spin chain.