Bethe-Salpeter equation for quantum-well exciton states in an inhomogeneous magnetic field

The trapping of excitons in a single quantum well due to the presence of a strong homogeneous magnetic field and a weak inhomogeneous cylindrical symmetric magnetic field, created by the deposition of a magnetized disk on top of the quantum well, both applied perpendicular to the $x-y$ plane of confinement is studied theoretically. The numerical calculations are performed for $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells and the formation of bound exciton states with nonzero values for the center-of-mass exciton wave function only in a small area is predicted.