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