here for the Hall current agrees with the result derived from the topological theory \[cf. Eq. (\[eq\_hall\])\].

So far I have said nothing about the quantization of the Hall current. Indeed, the above argument does not prove that the anomalous Hall conductivity precisely equals $\mp e^2/h$. It only indicates that $\sigma_{xy}$ is finite and predicts its sign. However, the argument does relate the anomalous Hall effect in graphene with periodic electromagnetic fields to the usual integer Hall effect in a constant magnetic field. It thus shows that the quantization of $\sigma_{xy}$ has the same origin in both cases.

Finally, a word on the nanotube system: The Hall effect found there[@Bel07] is not produced by states localized where the magnetic field has a well-defined direction, although such states are of course also present in that system. Rather it is produced by higher energy states that are localized where the magnetic changes sign. Thus, a different mechanism is responsible for the effect reported in Ref. . Other features also distinguish it from the Hall effect considered in the present work: It is not accompanied by a gap between the conduction and valence bands. It is associated with two sets of states on 