46 research outputs found
The long-range interacting Fermi polaron
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 which describes a self--interacting
impurity. In other dimensions, the impurity self--interacts with an infinite
number of its own images, and no bosonization occurs. We discuss applications
of our theory for the 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.Comment: 9 pages + 7 figure