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

Chapter 6
Critical Discussion and Future
Perspective
At first we address the topic of diffusive-ballistic crossover which was discussed in
Sec.4.5.1: The ansatz which was used to show a reduction of spin relaxation rate appearing
due to cubic Dresselhaus SOC, was a discretization of angles when summing over momenta
of the Cooperon. Although the constraint for the angles reduces the Cooperon eigenvalues
significantly, this ansatz is still based on linear response. One consequence is that contributions
appearing at low channel number and steaming from edge to edge skipping orbits, as
shown in Ref.[BvH88b], are not included. Such orbits can lead to flux cancellation effects,
which e.g. can weaken the magnetic field dependence of WL correction to the conductivity.
However, in further work we will show the reduction of spin relaxation rate dependence on
the number of transverse channels in the framework of a nonperturbative theory based on
the paper by S. Kettemann et al., Ref.[KM02]. In latter work the magnetic phase-shifting
rate 1/τ B has been identified with a correlation function of the magnetic vector potential.
In turn this correlation function is related to a term in the nonlinear σ-model which appears
due to time-reversal symmetry breaking. Thus, in case of an effective magnetic field due to
SOC, which brakes spin rotation symmetry, the respective term in the nonlinear σ-model
has to be identified to yield a nonperturbative expression for the spin relaxation rate 1/τ s .
The last chapter of this work stands out from the rest by the fact that the focus is more
on numerical calculations. The code was developed as general as possible by decomposing
all matrix operations in connectivity and hopping matrices including magnetic field and
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