Dc electrical current generated by upstream neutral modes

Quantum Hall phases are gapped in the bulk but support chiral edge modes, both charged and neutral. Here, we consider a circuit where the path from the source of electric current to the drain necessarily passes through a segment consisting solely of neutral modes. We find that upon biasing the source, a dc electric current is detected at the drain, provided there is backscattering between counterpropagating modes under the contacts placed in certain locations. Thus, neutral modes carry information that can be used to nonlocally reconstruct a dc charge current. Our protocol can be used to detect any neutral mode that counterpropagates with respect to all charge modes. Our protocol applies not only to the edge modes of a quantum Hall system, but also to systems that have neutral modes of nonquantum Hall origin. We conclude with a possible experimental realization of this phenomenon.