Anomalous Hall conductivity and quantum friction

The anomalous Hall effect in high conductivity region is studied using a two-dimensional network model. We find that the off-diagonal conductivity comprises two parts: one which reflects the bulk properties as obtained by the Kubo formula and another which is sensitive to boundary conditions imposed on the network. In the fully coherent limit, the latter scales with the width of the conducting channel, while for real-world samples, it is controlled by the coherence length. It provides an alternative interpretation of the observed behavior in the clean limit which is otherwise attributed to the skew scattering. We highlight analogies to friction in viscous fluids responsible for Couette flow. In the present case, this quantum effect is governed by wave interference.