Exciton Spin Dynamics in Semiconductor Quantum Wells

1.1 Two-Dimensional exciton fine structure The spin properties of excitons in nanostructures are determined by their fine structure. Before analysing the exciton spin dynamics, we give first a brief description of the exciton states in quantum wells. We will mainly focus in this review on GaAs or InGaAs quantum well which are model systems. For more details, the reader is referred to the reviews in ref. [1, 2]. As in bulk material, exciton states in II-VI and III-V quantum wells (QW) correspond to bound states between valence band holes and conduction band electrons. As will be seen later, exciton states are shallow two-particle states rather close to the nanostructure gap, i.e. their spatial extension is relatively large with respect to the crystal lattice, so that the envelope function approximation can be used to describe these states. The problem of exciton states in bulk crystals or nanostructures is in fact a N −electron problem, in which we seek for the stationary states of a crystal where one electron has been removed from the valence states and set in the conduction band, thus leaving N − 1 valence band electrons. Due to electron indiscernability, the latter states should be antisymmetrized. At this point it is more convenient to use the electron-hole pair states basis, ψ s,ke (r e)ψ h m,k h (r h) where ψ s,ke (r e) = 1 √ V e ike.re u s,ke (r e) is a conduction Bloch function (V being the crystal volume), and ψ h m,k h (r h) = 1 √ V e ik h .r h u m,k h (r h) is the hole function obtained by applying the time reversal operatorˆK to a corresponding electron valence state ψ mv ,kv (r). This description offers the advantage to give the possibility to solve the exciton problem as a two-body problem. This is done usually in two steps: first treat the Hartree type problem between a conduction electron and a hole with direct Coulomb attractive potential, thus yielding the so-called " mechanical " exciton, then solve by perturbation the corrections due to electron-hole exchange terms. Note these terms appear due to the non vanishing coulomb exchange terms arising between the conduction electron 2 Thierry Amand and Xavier Marie and the remaining N − 1 valence band electrons. A description of the exciton fine structure in bulk semiconductors can be found in [3]. In quantum wells …