Overlap structure of Fano-resonance profiles of excitons in a semiconductor quantum well

The Fano resonance of an exciton in a quantum well of ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ belonging to the ${\Gamma }_7^{+}$-irreducible representation is investigated based on the excitonic $4\times 4$ Luttinger Hamiltonian. Multichannel scattering problems for the resonance states are solved by virtue of the adiabatic expansion and the R-matrix propagation method, which enable us to implement high-resolution calculations without introducing any empirical broadening parameters. Absorption spectra for excitons are calculated in 100–$500-\AA$-thick quantum wells, and detailed Fano-resonance profiles for both optically active and inactive exciton states are revealed. Specifically, it is noticed that complicated interference between Fano resonances pertaining to different subbands occurs in a quantum well of more than $350\hspace{0.5em}\AA .$ A resulting composite profile manifests itself as overlap resonance, accompanying marked changes in a peak height, a width, and an asymmetry pattern from the corresponding isolated profiles. Such changes are evaluated qualitatively by use of Fano’s model for one open-channel and two closed-channels. Moreover, quantitative interpretations are also made by employing a time delay given by an eigenphase sum.