Landau levels of two-dimensional negatively charged three-particle Coulomb states

We study the influence of a low external uniform magnetic field on the energy levels of three-particle Coulomb states in a strictly two-dimensional medium. We show that at low magnetic fields, when the coupling between the relative motion and the motion of the centre of mass may be neglected, additional Landau levels appear. We compute the ground state energy corresponding to the relative motion as a function of the strength of the magnetic field for different values of the mass ratio of the negatively and positively charged particles. We compare our results with those we obtained previously in the three-dimensional limit.