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Spin-dependent electron scattering in 2D electron systems Aitor Mugarza Catalan Institute of Nanoscience and Nanotecnology (ICN2) Barcelona, Spain Nanospain, Donostia, March 9 th 2017
Spin-dependent electron scattering in 2D electron systemsAitor Mugarza
Catalan Institute of Nanoscience and Nanotecnology (ICN2)Barcelona, Spain
Nanospain, Donostia, March 9th 2017
-k s k
Spin locked to momentum
J(x) S(x)
Charge
current Spin
density
Rashba statesTopological states
-k s k
Spin locked to momentum
J(x) S(x)
Charge
current Spin
density
Rashba statesTopological states
-k s k
Spin locked to momentumJ(x) S(x)
Charge
current Spin
density
Scattering coefficients
Quantum mirage
Quantum invisibility
Heller Nature 369, 464 (1994)
Manoharan Nature 403, 512 (2000)
Fransson Nano Lett. 10, 1600 (2010).
Vacancy island on Ag(111)
Topo
ST
S
𝑒𝑖𝑘𝑥𝑟 𝑒−𝑖𝑘𝑥
𝑡 𝑒𝑖𝑘𝑥𝑡𝑟 𝑒𝑖𝑘𝑥
𝑡𝑟𝑟 𝑒𝑖𝑘𝑥
7
6
5
4
3
2
1
4002000
V (mV)
on flat Ag(111) terraceinside triangle
dI/
dV
(a.u
)
Quantum interference effects in a
potential well: standing waves and
discrete energy levels
Particle in a box
A. Mugarza et al. PRL 87, 3 (2001)F. Schiller et al., NJP 16, 123025 (2014)J. E. Ortega et al. PRB 87, 115425 (2013)J. E. Ortega et al., Handbook of Surface Science(Springer, coming son!)
Monoatomic steps on Ag(111)
|Y(x)|2
0 L
EF
V
Vbarrier
N=1
N=2
N=3
x
12nm
500ºC
12nm
550ºC
18nm
600ºC
27nm
625ºC
12nm
450ºC
S. J. Altenburg et al., PRL 108 (2012)
D. Subramaniam et al., PRL 108 (2012)
S. K. Hämäläinen et al., PRL 107 (2011)A. Garcia-Lekue et al., PRL 112, 066802 (2014)
A. Garcia-Lekue et al., PRL 112, 066802 (2014)
A. Garcia-Lekue et al., PRL 112, 066802 (2014)
A. Garcia-Lekue et al., PRL 112, 066802 (2014)
G
GG
G
•
•
𝑠𝑝 − SS
𝑑 − SR
Ag(111)
Bi (1/3 ML)
BiAg2
top view
side view
Band structure
Only intraband transitions!
FFT q(E) vs Theory
𝑞 = 𝑘𝑖 − 𝑘𝑓
pz px py
Δ𝐉 = Δ𝐋 +1
2Δ𝐒 = 0
𝑝𝑦, ↓ 𝐋 ⋅ 𝐒 𝑝𝑥 , ↑ ≠ 0
Different intensity
L. Bürgi et al., Phys. Rev. Lett. 81, 5370 (1998).
rl rr jl/p jr/p
A-step 0.70±0.30 0.21±0.07 -0.83±0.02 -0.95±0.02
B-step 0.40±0.18 0.36±0.15 -0.56±0.02 -0.51±0.02
strong resonator weak resonator
N=2
N=2
The Curved Surface Approach
d
Tunable
h, e-
Sample center
[hkl]
step parallel
[h’k’l’]
miscut range
º
c-X(hkl)
Curved surfaces allows to tune and achieve atomic scale control overphysical-chemical processes related to atomic steps
Scattering analysis framework: 1D Kronig-Penney model
d b
ytyr
yi
U0
2
*
2
01
2*
2
2
12
Em
bUtg
dmE
1D Kronig-Penney model
J. Lobo-Checa et al., unpublished
B-typeA-type
New scattering mechanism in spin-orbitronic materials
Controlled by chemical composition of steps
Lateral spin-filtering
Efficiency depends on edge structure
