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The construction of optimally localized Wannier functions (and Wannierfunctions in general) for a Chern insulator has been considered to beimpossible owing to the fact that the second moment of such functions isgenerally infinite. In this manuscript, we propose a solution to this problemin the case of a single band. We accomplish this by drawing an analogy betweenthe minimization of the variance and the minimization of the electrostaticenergy of a periodic array of point charges in a smooth neutralizingbackground. In doing so, we obtain a natural regularization of the divergingvariance and this leads to an analytical solution to the minimization problem.We demonstrate our results numerically for a particular model system.Furthermore, we show how the optimally localized Wannier functions provide anatural way of evaluating the electric polarization for a Chern insulator.

Optimally Localized Wannier Functions for 2D Chern Insulators