Internal transitions of confined neutral magnetoexcitons in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells

Optically detected resonance spectroscopy has been used to study resonant absorption of electrons, holes, and their complexes in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells (QW’s) in magnetic fields up to 15 T. In undoped multiple-QW samples with well widths of 12.5, 15, and 20 nm, in addition to an electron and two hole cyclotron resonances, $1\overrightarrow{s}{\mathrm{np}}_{+,-}$ (in the hydrogenic notation) internal exciton transitions (IET’s) arising from two distinct neutral heavy-hole magneto-excitons were observed. The unique capability of observing electron and hole cyclotron resonance as well as several IET’s in a single sample permitted verification of a predicted relationship resulting from the symmetry of the magnetoexciton Hamiltonian, namely, $ħ({\omega }_e-{\omega }_h{)=E}_{{1s-np}_{+}}-E_{{1s-np}_{-}},$ where ${\omega }_e\left({\omega }_h\right)$ is the electron (hole) cyclotron frequency, and $E_{{1s-np}_{+}}$ ${(E}_{{1s-np}_{-}})$ is the energy of the $1\overrightarrow{s}{\mathrm{np}}_{+}$ $\left(1\mathrm{}\overrightarrow{s}{\mathrm{np}}_{-}\right)$ transition.