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

114 List of Figures
5.6 (a) DOS of a system of size L 2 = 40 2 with Rashba SOC, α 2 = 0.8t calculated
with exact diagonalization with cutoff η = 0.0215 (blue) and KPM with
M = 500 moments. (b) Relation between number of moments M and cutoff η. 98
5.7 (a) Averaged DOS ρ avr calculated with KPM (30 impurity configurations)
for system size of L 2 = 280 2 with Rashba SOC α 2 = 0.5t, for different
impurity strengths: V = 1t(black), V = 4t(red), V = 6t(green), V =
8t(blue) (b) Monotoneous reduction of typical DOS ρ typ with system size
L = 70, 140, 200, 280, for impurity strength V = 8t. . . . . . . . . . . . . . 100
5.8 (a) Log-plot of typical DOS ρ typ at V = 8t for different system sizes L with
Rashba SOC α 2 = 0.5t at half filling, calculated with KPM. The dashed line
isalinearfittothelog-data whichyieldsalocalization lengthofξ ≈ 100a. (b)
Localization length ξ at E F = 0, plotted as a function of impurity strength V.101
5.9 Finite size analysis of the typical DOS in relation to the averaged one,
ρ typ /ρ avr , here plotted for E F = 0: The system size has been changed with
L = 70, 140, 200, 280. The impurity strength for the different curves is given
by V/t = 1,3,4,5,6,8 (monotone from top to bottom). . . . . . . . . . . . . 102
5.10 a)+b) Matrix element density function j(x,y) for a clean system with 70×70
sites and pure Rashba SOC of strength α 2 = 1t using the analytical solution
Eq.(5.20). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.11 SHC σ SH (E F ,M) calculated with KPM for a system with 70×70 sites, pure
Rashba SOC of strength α 2 = 1t and M = 200 moments (blue curve). For
comparison the analytical solution is plotted (red curve), corresponding to
Fig.5.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
C.1 Weak localization correction in 2D in units of (2e 2 /2π). The parameters are
c 1 = 1/D e Q 2 SOτ ϕ and c 2 = 1/D e Q 2 SOτ. Thick line indicates ∆σ = 0. . . . . . 143