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

List of Figures 113
4.2 The spin dephasing time T 2 of a spin initially oriented along the [001] direction
in units of (D e q2 2 ) for the special case of equal Rashba and lin. Dresselhaus
SOC. The different curves show different strength of cubic Dresselhaus
in units of q s3 /q 2 . In the case of finite cubic Dresselhaus SOC we set
W = 0.4/q 2 . If q s3 = 0: T 2 diverges at θ = (1/4 + n)π, n ∈(dashed
vertical lines). The horizontal dashed line indicated the 2D spin dephasing
time, T 2 = 1/(4q2 2D e). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Example of an experiment done by Kunihashi et al.[KKN09]. The width dependence
of the spin relaxation length l 1D
SO
of different carrier density. Solid
lines and dashed lines in (b) show the l 1D
SO
calculated from the theory presented
in this work, with neglecting cubic Dresselhaus term and taking into
account full SOIs, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4 The lowest eigenvalues of the confined Cooperon Hamiltonian Eq.(4.49),
equivalent to the lowest spin relaxation rate, are shown for Q = 0 for different
number of modes N = k F W/π. Different curves correspond to different
values of α 2 /q s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 The lowest eigenvalues of the confined Cooperon Hamiltonian Eq.(4.49),
equivalent to the lowest spin relaxation rate, are shown for Q = 0 for different
number of modes N = k F W/π. Different curves correspond to different
values of α 1 /q s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1 Energy band E − (k), Eq.(5.10) is plotted for pure Rashba SOC as function
of wave vector k. The contour lines indicate the energy at which one finds a
Van Hove singularity in the DOS (below half-filling). . . . . . . . . . . . . . 87
5.2 (a) SHC σ SH as a function of Fermi energy E F , in a clean system of size
L 2 = 170×170 with both Rashba and linear Dresselhaus SOC with α 2 > α 1
(blue curve) and α 2 < α 1 (red curve). (b) SHC σ SH as a function of Fermi
energy E F , in a clean system of size V = 150×150 with only Rashba SOC
of strength α 2 = 0.8t (blue/solid), α 2 = 1.4t (red/dotted) and α 2 = 2t
(yellow/dashed). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3 DOS, as a function of Fermi energy in units of t, in presence of impurities
of binary type with a concentration of 10% calculated using exact diagonalization.
The system size is L 2 = 32 2 , and the SOC is Rashba type with
α 2 = 1.2t with cutoff η = 0.02t. . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4 (a) SHC, as a function of Fermi energy in units of t, in presence of impurities
of binary type calculated using exact diagonalization. The impurity strength
is V = −2.8t with a concentration of 10%. The system size is L 2 = 32 2 , and
the SOC is Rashba type with α 2 = 1.2t with cutoff η = 0.06. (b) Comparison
of a) with DOS (blue curve). . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.5 SHC σ SH as function of filling n in presence of impurities of binary type calculated
using exact diagonalization. The impurity concentration is set to 10%
for all plots and the average is performed over 200 impurity configurations.
The system size is L 2 = 32 2 , and the SOC is Rashba type with α 2 = 1.2t
with cutoff η = 0.06 (a) V = −0.2t...−2.8t (b) V = −2.8t...−5t. . . . . 95