Catalan Institute of Nanoscience and Nanotecnology … · Spin-dependent electron scattering in 2D electron systems Aitor Mugarza Catalan Institute of Nanoscience and Nanotecnology

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