Exciton spectra in disordered quantum wells

We study the effects of disorder on the exciton spectra in quantum well (QW) semiconductor structures. We model the disorder by introducing the fractional Laplacian into the Schrödinger equations, which describe the exciton spectra of the above QW structures. We calculate the exciton binding energies in its ground state and a few low-lying excited states as a function of the GaAs QW size. Our main finding is that disorder significantly increases the exciton binding energy in QWs, sometimes by a factor of 10. For disordered case, the interplay between strength of disorder (characterized by Lévy index α in our approach) and nonzero exciton angular momentum in its excited states causes the system to perceive QW finite physical barrier heights as infinite, which also influences the exciton binding energy. Our results can be applied for heterostructures like GaAs/AlGaAs, GaN/AlGaN, as well as to any of the II-VI and III-V heterostructures, which may be used in many optoelectronic and spintronic applications.