Multiband Electronic Structure of Magnetic Quantum Dots: Numerical Studies

Abstract

Semiconductor quantum dots (QDs) doped with magnetic impurities have been a focus of continuous research for a couple of decades. A significant effort has been devoted to studies of magnetic polarons (MP) in these nanostructures. These collective states arise through exchange interaction between a carrier confined in a QD and localized spins of the magnetic impurities (typically: Mn). Our theoretical description of various MP properties in self-assembled QDs is discussed. We present a self-consistent, temperature-dependent approach to MPs formed by a valence band hole. The Luttinger-Kohn k ¤ p Hamiltonian is used to account for the important effects of spin-orbit interaction.

Circular Polarization Dynamics during Magnetic Polaron Formation in Type-II Magnetic Quantum Dots

“…Here, β is the hole-Mn exchange coupling constant ( m J = ± J z , J z = 3/2), S zj is the z -projection of the Mn spin ( S = 5/2) at position R j , |ψ MP ( R j )| 2 is the overlap of the heavy-hole envelope function at the Mn site, μ B is the Bohr magneton, N Mn is the number of Mn ions in the dot, and g h ( g Mn ) is the hole (Mn) g -factor. We model the heavy-hole envelope function as the ground-state solution of a 2D harmonic oscillator in the x – y plane, times a normalized cosine along the z -axis. ,, where L MP is the lateral width of the wave function, r 2 = x 2 + y 2 , and h is the height of the quantum dot. The hole localization diameter can be smaller than the QD diameter d ′.…”