I'm confused about the conductivity and the edge states in the IQHE. On the plateaux, we zero the longitudinal conductivity and resistivity, right? So is it really true, that on the plateaux, there is no current flowing in the longitudinal direction, only in transverse?
From this image, it looks to me, that the edge states carry the current in longitudinal direction and that there is no current flowing in transverse direction. What did I miss understand?