lattice constant are applied jointly to a graphene sample. Since these fields have a periodicity $\gg 1$Å, experimental realization is more feasible than in the case of Haldane’s model. In this paper I show analytically that the resulting gapped state is of the same anomalous type as in Haldane’s model. Apart from being experimentally relevant, the system studied here has another interesting feature. Its Hall effect can be explained without recourse to the topological theory. Because of this it is possible in the present instance to identify a physical mechanism responsible for the Hall effect. This hopefully takes some of the mystery out of the general but abstract topological theory.[@Kar54; @Thou82; @Thou85; @Sim83a; @Sim83b; @Koh84; @Osh94; @Ono01; @Hal04]

A gapped graphene state that results from smoothly varying fields was first revealed in the numerical study of Ref. (see Figure 2, last frame, of that work) and is also mentioned in Ref. . The effective magnetic field studied in these references is produced by lattice deformations. The single-valley physics of such a field is identical to that of a real magnetic field. The analytical results for a single valley that is presented here confirm and explain numerical results obtained in Refs. 