Quasi-two-dimensional excitons in finite magnetic fields

We present a theoretical and experimental investigation of the effects of a magnetic field on quasi-two-dimensional excitons. We calculate the internal structures and dispersion relations of spatially direct and indirect excitons in single and coupled quantum wells in a magnetic field perpendicular to the well plane. We find a sharp transition from a hydrogenlike exciton to a magnetoexciton with increasing the center-of-mass momentum at fixed weak field. At that transition the mean electron-hole separation increases sharply and becomes $\propto {P/B}_{\perp },$ where P is the magnetoexciton center-of-mass momentum and $B_{\perp }$ is the magnetic field perpendicular to the quantum well plane. The transition resembles a first-order phase transition. The magnetic-field–exciton momentum phase diagram describing the transition is constructed. We measure the magnetoexciton dispersion relations and effective masses in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.33}{\mathrm{Ga}}_{0.67}\mathrm{As}$ coupled quantum wells using tilted magnetic fields. The calculated dispersion relations and effective masses are in agreement with the experimental data. We discuss the impact of magnetic field and sample geometry on the condition for observing exciton condensation.