Change of Hall conductance induced by band crossing

We investigate the change of Hall conductance induced by band crossing in the Hofstadter spectrum. Numerical study shows that, if the magnetic flux is (Formula presented) flux quanta per plaquette, then the change of the Hall conductance is (Formula presented) or 0, depending on whether the energy dispersion near degenerate points is linear or quadratic. This is consistent with an earlier study by Bellissard (cond-mat/9504030, unpublished). We also find that the change of the Hall conductance is accompanied by the “transport” of a daughter subband between the degenerate parent bands. A semiclassical explanation of this subtle effect is offered.