  We theoretically investigate exciton-polaritons in a two-dimensional (2D)
semiconductor heterostructure, where a static magnetic field is applied
perpendicular to the plane. To explore the interplay between magnetic field and
a strong light-matter coupling, we employ a fully microscopic theory that
explicitly incorporates electrons, holes and photons in a semiconductor
microcavity. Furthermore, we exploit a mapping between the 2D harmonic
oscillator and the 2D hydrogen atom that allows us to efficiently solve the
problem numerically for the entire Rydberg series as well as for the
ground-state exciton. In contrast to previous approaches, we can readily obtain
the real-space exciton wave functions and we show how they shrink in size with
increasing magnetic field, which mirrors their increasing interaction energy
and oscillator strength. We compare our theory with recent experiments on
exciton-polaritons in GaAs heterostructures in an external magnetic field and
we find excellent agreement with the measured polariton energies. Crucially, we
are able to capture the observed light-induced changes to the exciton in the
regime of very strong light-matter coupling where a perturbative coupled
oscillator description breaks down. Our work can guide future experimental
efforts to engineer and control Rydberg excitons and exciton-polaritons in a
range of 2D materials.
