Effect of size and shape dispersion on the averaged magnetic response of ensembles of semiconductor quantum rings

In this paper a theoretical study was made of the conditional averages of the magnetization and magnetic susceptibility of dispersive ensembles of nano-objects with a very complex geometry---self-assembled wobbled semiconductor quantum rings. Using the multivariate statistics approach and previously proposed mapping method the impact of the dispersion of the ring geometry parameters on the static magnetic response of the ensembles has been investigated near the first Aharonov-Bohm oscillation. The description is suited to clarify the important question of which geometrical parameters' dispersions are crucial for the formation and properties of the magnetic response of ensembles. We theoretically show that for the dispersive ensembles of InGaAs/GaAs capped wobbled quantum rings the actual value and temperature dependence of the differential magnetic susceptibility can be optimized by an appropriate control of the conditional parameters of the ensembles. The ring rim radius variations play a crucial role in this dependence. We have managed to simulate in detail the temperature behavior of the meaningful averages of the magnetization and positive peak of the differential magnetic susceptibility for ensembles of the rings known from the experiment. The simulated temperature dependence, position, and magnitude of the positive peak in the differential magnetic susceptibility are in a good agreement with the experimental observations.