NTT Basic Research Laboratories

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The University of Hong Kong, August (2005)
Transport in Mesoscopic Systems Affected by the
Rashba Spin-Orbit Interaction

• Rashba spin-orbit interaction
• Stern-Gerlach spin filter
• Spin interference experiment

NTT Basic Research Laboratories
Junsaku Nitta
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The Rashba spin-orbit interaction
Structural inversion asymmetry (SIA)
Ez0
Spin degeneracy is lifted by gate voltage
Vg2
Ez gt0
Spin configuration at EF
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Control of SOI in InGaAs Quantum Wells
InGaAs QW
asymmetric
Weak anti-localization
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T0.3K
1
2
2
3
3
4
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N1N2 const. Same Rxx at B 0
symmetric
Gate Electric fields Vg
Weak localization
Gate voltage can control the Rashba SOI.
Phys. Rev. Lett. 89, 046801(2002)
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Control of SOI and spin precession
Very similar to the top
Japanese traditional top
Beff
Beff
ltlt
Large
Small
Spin-orbit interaction
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Transverse force on spins
Rashba Hamiltonian
Transverse Force by S. Q. Shen
Force on sz and -sz is opposite direction
z
Science, G.W. Bauer
However, sz is not conserved quantity
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Stern-Gerlach experiment (1922)
Difficulty of charged particles because of
Lorentz force
Gradient of magnetic field
http//www.physicstoday.org/
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Problem of Stern-Gerlach experiment with charged
particles
Bz is non zero since
Maxwell eq.
Uncertainty of deflection angle DfSG
d QW thickness
Difficult to satisfy with
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S-G exp. based on the Rashba SOI
Ando model including SOI
T. Ando, Phys. Rev. B40, 5325 (1989)
qmax 0.02p, Da 0.64x10-11 eVm
Spatial Gradient of SOI
Gradient of SOI
Initial wave packet
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Spin filter due to the S-G effect
Charge density
Spin density
Phys. Rev. B72, 041308(R) (2005)
Collaboration with prof. T. Ohtsuki group
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Spin Filter Operation by Gate Voltage

sy is spatially separated
Beff
Vg1
y
Vg2
x
Spatial gradient of SOI

• Features
• Without magnetic fields and ferromagnets
• Spin direction can be controlled by Vg

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Fabrication of SG-spin filter
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Neutron Spin-interference Exp.
4p-spin precession 2p-phase shift
Interference
1 cm
Si crystal
H. Rauch et al Phys. Lett. 54A (1975)
Spin precession Local magnetic field
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Spin interferometer by the Rashba SOI
Vg 0 V
Vg 1 V
Ring conductance depends on the precession angle
Spin interference device
Appl. Phys. Lett. 75, 695 (1999)
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Aharonov-Bohm Oscillations Sample specific feature
Detail of the trajectory and kF affect the
interference
h/e period oscillations
AB oscillations
Gate voltage changes kF , and its interference
pattern !
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AAS effect Time-reversal symmetry interference
AAS oscillation does not depend on wave-vector
kF But it depends on spin precession angle
Wave-function
Orbital phase
Spin phase
h/2e period oscillations
Phase difference 0
Trajectory Same length between cw and anti-cw
Always constructive
Constructive/Destructive
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Sample specific h/e oscillations are reduced by
ensemble averaging
1 mm
2 mm
A single ring
Array of rings
Time reversal symmetric h/2e oscillations
survives after ensemble averaging
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Vg dependence of AAS oscillations
Array of 7700 loops
Gate voltage
Array of loops is covered with gate to control SOI
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Gate controlled SOI and spin precession
Weak anti-localization
Gate voltage dependence of SOI
Spin interference
Experimental demonstration of Aharonov-Casher
Effect
Cond-mat/0504743
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Summary
Mesoscopic version of Stern-Gerlach experiment
Spin interference experiment based on the
Rashba SOI
Stern-Gerlach Exp.
Spin interference Exp.
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Acknowledgement
Stern-Gerlach spin filter J. Ohe (Sophia
University) M. Yamamoto (Sophia University) T.
Ohtsuki (Sophia University) T. Kobayashi (NTT
BRL) Spin interference experiment T. Koga
(Hokkaido University) Y. Sekine (NTT BRL) C.
Schierholtz (NTT BRL) F. Meijer (Delft
University)
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Spin precession by the Rashba SOI
Spin splitting as if a spin feels an effective
magnetic field perpendicular to it momentum
direction
Beff
EF
Spin precession and precession angle
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Uncertainty of SG deflection angle
Deflection angle uncertainty
FL(top) gtFL(bottom)
z
d
y
x
vF
DfSG
FL(top)
fSG
FL(bottom)
x
y
tDt
t0
The difference in Lorentz force between top and
bottom in QW leads to spread of wave packet.
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Ensemble averaging of AB oscillations
N 3
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Transfer Matrix calculation of the Landauer
conductance
at E/V03.0