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We consider a half-filled Chern band and its transport properties in twophases that it may form, the electronic Fermi liquid and the composite-fermionFermi liquid. For weak disorder, we show that the Hall resistivity for theformer phase is very small, while for the latter it is close to $2h/e^2$,independent of the distribution of the Berry curvature in the band. At risingtemperature and high frequency, we expect the Hall resistivity of theelectronic phase to rise, and that of the composite-fermion phase to deviatefrom $2h/e^2$. At high frequency, sign changes are expected as well.Considering high-frequency transport, we show that the composite fermion phasecarries a gapped plasmon mode which does not originate from long ranged Coulombinteraction, and we show how this mode, together with the reflection ofelectro-magnetic waves off the Chern band, allow for a measurement of thecomposite-fermion Drude weight and Berry curvature. Finally, we consider ascenario of a mixed-phase transition between the two phases, for example as afunction of displacement-field, and show that such transition involves anenhancement of the longitudinal resistivity, as observed experimentally.

Transport properties of a half-filled Chern band at the electron and composite fermion phases