Hall Drag in Correlated Double Layer Quantum Hall Systems

We show that in the limit of zero temperature, double layer quantum Hall systems exhibit a novel phenomena called Hall drag, namely a current driven in one layer induces a voltage drop in the other layer, in the direction perpendicular to the driving current. The two-by-two Hall resistivity tensor is quantized and proportional to the $\mathbf{K}$ matrix that describes the topological order of the quantum Hall state, even when the $\mathbf{K}$ matrix contains a zero eigenvalue, in which case the Hall conductivity tensor does not exist. Relation between the present work and previous ones is also discussed.