Seminarium Fizyki Materii Skondensowanej

We construct the simplest density functional for the problem of a single impurity interacting with a Fermi gas via a long–ranged potential using the Thomas–Fermi approach. We find that the Fermi polaron is fully bosonized in two dimensions, as the model results in a suitable Landau–Pekar functional known from the Bose polaron problem, and its multi—imaged version in other dimensions. We discuss applications of our theory for the 2d exciton–polaron and the ionic polaron problem and compute the effective mass for these cases, finding a self–trapping transition with order depending on the dimensionality.