Chern Bands' Optimally Localized Wannier Functions and Fractional Chern Insulators

Recent development on fractional Chern insulators and proximate phases call for a real space representation of isolated Chern bands. Here we propose a new method for a general construction of optimally localized Wannier functions from such Chern bands. We do so through an optimal gauge choice of the Bloch states of a Chern band with the singularity placed at any desired position in momentum space. We apply this method to construct the optimally localized Wannier functions for kagome lattice, and use it to identify channels of interactions that are favorable to the development of fractional Chern insulators. Implications of the approach for the interplay between correlations and topology in broader contexts are discussed.