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

4 Chapter 1: Introduction
both the elastic mean-free path l e and λ F is in addition motivated by the fact that recently
it could be observed with optical[HSM + 06] as well as with measurements of the change in
magnetoconductivity.[DLS + 05, LSK + 07, SGP + 06, WGZ + 06, KKN09]
We have a tool to study such dephasing and symmetry-breaking mechanisms in
conductors[AAKL82, Ber84, CS86]: It is the quantum interference of electrons in lowdimensional,
disordered conductors. We will show in Chapter3 how this effect results in
corrections to the electrical conductivity ∆σ, which is known as weak localization (WL)
effect. Obviously also here we focus on systems with entanglement of spin and charge by
SO interaction. The SO field, which has various forms in the semiconductor, makes the
effect richer because it can enhances the conductivity by reversing the effect of WL. This
is called weak antilocalization (WAL). We are going to calculate the correction with the
Cooperon equation. Due to the fact that the origin of the interference-suppression is the
randomization of the spin, more precise, the D’yakonov and Perel’ spin relaxation in this
work, it seems natural to establish a connection between the spin diffusion picture, e.g
derived from the Eilenberger equation by Schwab et al.[SDGR06], and the local correction
described by using the Cooperon equation, as we are going to shown in Sec.3.3. The link
to applications in the field of spintronics is a better insight in what possibilities we have to
create long living spin modes which will appear as special cases in our calculation.
As mentioned, the addition of boundaries can change the spin relaxation significantly.
The change depends of kind and direction of the wire boundaries. Chapter4 will
focus especially on the latter. The connection between the WL and the spin diffusion will
help us to understand both at the same time: The magnetoconductivity and the existence
of persistent spin states for a given wire.
Having derived a consistent theory of spin relaxation in quantum wires, one could wonder
why there are measurements of spin lifetime, like done by Kunihashi et al.[KKN09] in gatefitted
narrowwiresfrommagnetotransport experiments, whichshowdeviations fromtheory.
This happens although all dominant SO coupling (SOC) types, namely linear Rashba and
lin. and cubic Dresselhaus SOC, have been included in the theory. The crucial point is: If
a part of the SOCs is left out, i.e. the cubic Dresselhaus SOC, one has great accordance between
experiment and theory. In Chapter4 we are going to show how this puzzle is resolved
by doing a crossover from the diffusive to the ballistic regime and revealing a suppression
of the problematic terms.