Scattering of low-energy fermions by a background of Chern-Simons vortices

We consider the interaction of (2+1)-dimensional fermions with a background of a charged-vortex solution of the Chern-Simons-Higgs model. When the fermions are coupled in the minimal way to the vortex gauge fields, the interaction potentials contain short-range terms, related to the vortex electric and magnetic field, and long-range terms, proportional to the topological charge of the vortex, that modify the centrifugal barrier. As a consequence of this inverse-square tail, at a large distance from the center of the vortex, the fermion behaves as if it had an effective angular momentum that, because of the difference between the fermion charge e and the scalar charge q, can assume any rational value. We develop a procedure to study the scattering of low-energy fermions by any kind of vortex and with a partial-wave analysis we compute, for any value of the fermion angular momentum, the phase shifts, the Jost functions, and the scattering cross sections. The obtained results crucially depend on the quantity en/q (n being the vorticity) and the low-energy cross section diverges at zero momentum.