Itinerant Spin Dynamics in Structures of ... - Jacobs University

Chapter 2: Spin Dynamics: Overview and Analysis of 2D Systems 7
Figure 2.1: Schematic representation of the band structure of GaAs around the Γ point
(extracted from Ref.[Bur08]).
on the energy band structure. Using the Kane Model it can be shown that the SOC due
to lattice-periodic potential leads to a lifting of degeneracy with a gap ∆ SO = 3/(4λ) (with
λ form Eq.(2.3)) between the Γ 8v states describing heavy and light holes and Γ 7v states,
as sketched in Fig.2.1 where Γ 7v is represented as the split-off band.[DR93, Win04a] It is
important to notice that in the following we do not focus on the SOC which is due to strong
Coulomb potential of the atomic core regions, but on the appearance of SO effect in the
conduction band due to additional external electric field and spatial symmetry breaking as
explained in more detail in the next sections. Notice that the effects we present in this work
are therefore on a different energy scale: The Pauli splitting ∆ SO can be large, 0.34 eV in
GaAs, compared to splitting at the conduction band which is on the order of meV in GaAs.
Before we review the spin dynamics of conduction electrons and holes in semiconductors
and metals, let us first reconsider the spin dynamics of a localized spin, as governed by the
Bloch equations.