  One starts from a planar Maxwell-Chern-Simons model endowed with a
Lorentz-violating term. The Dirac sector is introduced exhibiting a Yukawa and
a minimal coupling with the scalar scalar and the gauge fields, respectively.
One then evaluates the electron-electron interaction as the Fourier transform
of the Moller scattering amplitude carried out in the non-relativistic limit.
In the case of a purely time-like background, the interaction potential can be
exactly solved, exhibiting a typical massless behavior far from the origin. The
scalar interaction potential is always attractive whereas the gauge
intermediation may also present attraction even when considered in the presence
of the centrifugal barrier and the A^{2} term. Such a result is a strong
indication that electron-electron bound states may appear in this theoretical
framework.
