Density Functional Theory of Composite Fermions

We construct a density functional theory for two-dimension electron (hole) gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the systems form composite fermion liquids. Our theory provides a systematic and rigorous approach to determine the properties of ground states in fractional quantum Hall regime modified by artificial structures. We also propose a practical way to construct approximated functional.