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Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China.

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Understanding the values and origin of fundamental physical constants, one of the grandest challenges in modern science, has been discussed in particle physics, astronomy and cosmology. More recently, it was realized that fundamental constants have a biofriendly window set by life processes involving motion and flow. This window is related to intrinsic fluid properties such as energy and length scales in condensed matter set by fundamental constants.

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We consider a half-filled Chern band and its transport properties in two phases that it may form: the electronic Fermi liquid and the composite-fermion Fermi liquid. For weak disorder, we show that the Hall resistivity for the former 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 rising temperature and high frequency, we expect the Hall resistivity of the electronic phase to rise, and that of the composite-fermion phase to deviate from 2h/e^{2}.

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