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

78 Chapter 4: Direction Dependence of Spin Relaxation and Diffusive-Ballistic Crossover
can also support the method proposed in Ref.[SKK + 08] -to determine the relative strength
of Rashba and Dresselhaus SOC from WL/WAL measurements without fitting parameterswith
inclusion of cubic Dresselhaus term for wire directions different from [100] and [010]
in an analytical manner.
In the (110) system the situation is different: In the 2D case it was shown by Pikus et al.,
Ref.[HPB + 97], that in the absence of the Rashba terms the negative magnetoconductivity
cannot be observed. In the case of a wire geometry we can conclude from Eqs.(4.41-4.46)
that we have no width dependence if Rashba SOC vanishes. A change of the quantum
correction to the static conductivity therefore cannot be achieved in this wire geometry by
changing the wire width. The reason is the vector potential in the boundary condition,
Eq.(4.40), which only depends on the Rashba SOC.
4.5 Diffusive-Ballistic Crossover
In the following we assume a (001) 2D system with both, Rashba and linear and
cubic Dresselhaus SO coupling.
Experiments measuring WL in diffusive quantum wires with SOC[LSK + 07, SGB + 09] are in
great agreement with theoretical calculations by S. Kettemann, Ref.[Ket07]. But considering
e.g. the works Ref.[KKN09, KHG + 10], one realizes that the scope of application of the
theory has to be extended to describe also the crossover to the ballistic regime, l e > W. In
Fig.4.3 we show an example of an experiment done by Kunihashi et al.[KKN09]. The lines
show a fit using Eq.(10) in the paper by S. Kettemann[Ket07] which is equal to the results
presented in Sec.4.2.2 if the width dependence of the term due to cubic Dresselhaus SOC
is neglected. To get the solid lines the term due to cubic Dresselhaus SOC was neglected,
the dashed include it. When checking Fig.4.3 (a) the condition l e < W is not fulfilled at all
wire width. It follows that this additional term is suppressed if the condition of a diffusive
system does not hold anymore.
We have shown in Sec.4.2.2 that the presence of cubic Dresselhaus SOC in the
sample leads to a finite spin relaxation even for wire widths Q SO W ≪ 1, regardless of the
boundary direction in a (001) system. To account for the ballistic case we have to modify
the derivation of the Cooperon Hamiltonian, Eq.(4.5). In the case of a wire where the mean