Transcript Spin Hall Effect

SPIN-HALL EFFECT
a new adventure in condensed matter physics
JAIRO SINOVA
San Houston State University, January 22th 2008
Research fueled by:
NERC
Mario Borunda Sergio Rodriguez
Xin Liu
Alexey Kovalev Nikolai Sinitsyn
Texas A&M U. Texas A&M U.
Texas A&M U. Texas A&M U. Texas A&M U.
U. of Texas
Tomas Jungwirth
Inst. of Phys. ASCR
U. of Nottingham
Allan MacDonald
U of Texas
Joerg Wunderlich Laurens Molenkamp
Wuerzburg
Cambridge-Hitachi
Ewelina Hankiewicz
U. of Missouri
Texas A&M U.
Kentaro Nomura
U. Of Texas
Branislav Nikolic
U. of Delaware
Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo,
Dimitri Culcer , Qian Niu, S-Q Shen, Brian Gallagher, Tom
Fox, Richard Campton, Winfried Teizer, Artem Abanov
OUTLINE


From electronics to spintronics:
 Electron multipersonality: using the charge and using the spin
 Success stories of metal based spintronics
 Why semiconductor spintronics may be better
 Spin-orbit coupling: the necessary evil
 The usual example: Das-Datta transistor
Spin-Hall effect:
 Normal and anomalous Hall effect and Spin Hall effect










Three contributions to the AHE
Turbulent history of the AHE
Recent focus on the intrinsic AHE
Application to the SHE
Short but turbulent history of the SHE
SHE experiments
Resolution of some of the controversy
Spin Hall spin accumulation
Theory challenges
Experimental challenges
What is spintronics?
ELECTRONICS
CHARGE
Mr. Electron
Two parts to his
personality !
SPIN
UP TO NOW: all electronics are mostly based
on the manipulation of the charge of the electron
so perhaps we should say “charge electronics”
SPINTRONICS: manipulate spin and
charge simultaneously
Using the charge
the field effect transistor:
work horse of information processing
Vg >0
ALL computers have these
transistors in one form or another
S
gate
insulator
- - - - - semiconductor
substrate
HIGH tunablity of electronic transport
properties the key to FET success in
processing technology
thin free charge carrier
channel induced by
electric field from gate
High mobility 2DEG: IQHE, FQHE, MIT, etc.
D
Using the spin
ferromagnetism:
work horse of information storing
1st generation spintronic devices based on
ferromagnetic metals: GMR– already in every computer
GMR  allowed read-out heads in hard drives to be MUCH smaller
Magnetic tunneling junction
(MTJ) or “spin valve” 
Nonvolatile MRAM: “Microchips
that never forget ”
Compatibility with Si and GaAs  next
phase: semiconductor spintronics, a
marriage of convenience!!!
A brighter future with semiconductor spintronics
Can do what metals do
- GMR, TMR in diluted magnetic semi-cond., spin transfer, etc.
Easy integration with semiconductor devices
- possible way around impedance mismatch for spin injection.
More tunable systems
- transport properties: carrier concentration is tuned by gates
and chemical doping
- ferromagnetic state affected by carrier concentration (DMS)
- optical control of non-equilibrium populations
Possibility of new physical regimes/effects
- TAMR
- tunable spin-orbit coupling
MORE KNOBS = MORE PHYSICS
Necessities in performing
spintronics in semiconductors
Spin-generation: “spin battery”
- injection (conventional)
- optical, via selection rules (excitation with circular polarized light)
- via SO coupling (e.g., occupation-asymmetry in k-space, Spin Hall effect)
Spin-manipulation
- external magnetic field
- via SO coupling (e.g. Datta Das Spin-transistor)
Spin-detection: “spin meter”
- Magnetoresistive measurement (conventional)
- optical, via selection rules (Spin LED)
- via SO coupling (e.g., anomalous Hall effect)
Spin-orbit coupling interaction
(one of the few echoes of relativistic physics in the solid state)
Ingredients: -“Impurity” potential V(r)
- Motion of an electron
Produces
an electric field

1
E   V (r )
e
In the rest frame of an electron
the electric field generates and
effective magnetic field


 k  
 E
Beff  

 cm 
This gives an effective interaction with the electron’s magnetic moment
H SO


 
 eS   k  1 dV (r ) 
 r
    Beff  
   S  L

 mc   mc  er dr 
CONSEQUENCES
•If part of the full Hamiltonian quantization axis of the spin now
depends on the momentum of the electron !!
•If treated as scattering the electron gets scattered to the left or to
the right depending on its spin!!
Using SO: Datta-Das spin FET
V/2
V
-
v
v
-
Beff
Beff
Datta-Das spin FET: the movie
Movie created by Mario Borunda
OUTLINE


From electronics to spintronics:
 Electron multipersonality: using the charge and using the spin
 Success stories of metal based spintronics
 Why semiconductor spintronics may be better
 Spin-orbit coupling: the necessary evil
 The usual example: Das-Datta transistor
Spin-Hall effect:
 Normal and anomalous Hall effect and Spin Hall effect










Three contributions to the AHE
Turbulent history of the AHE
Recent focus on the intrinsic AHE
Application to the SHE
Short but turbulent history of the SHE
SHE experiments
Resolution of some of the controversy
Spin Hall spin accumulation
Theory challenges
Experimental challenges
SPIN HALL EFFECT
A NEW TWIST ON AN OLD HAT
References:
N. A. Sinitsyn, J.E. Hill, Hongki Ming, Jairo Sinova, and A. H. MacDonald, Phys. Rev. Lett. 97, 106804 (2006)
Jairo Sinova, Shuichi Murakami, S.-Q. Shen, Mahn-Soo Choi, Solid State Comm. 138, 214 (2006).
K. Nomura, J. Wunderlich, Jairo Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Phys. Rev. B 96, 076804 (2006).
B. Kaestner, J. Wunderlich, Jairo Sinova, T. Jungwirth, Appl. Phys. Lett. 88, 091106 (2006).
K. Nomura, Jairo Sinova, N.A. Sinitsyn, and A. H. MacDonald, Phys. Rev. B. 72, 165316 (2005).
E. M. Hankiewicz, Tomas Jungwirth, Qian Niu, Shun-Qing Shen, and Jairo Sinova, Phys. Rev. B.72, 155305 (2005).
N.A. Sinitsyn, Qian Niu, Jairo Sinova, K. Nomura, Phys. Rev. B 72, 045346 (2005).
Branislav K. Nikolic, Satofumi Souma, Liviu P. Zarbo, Jairo Sinova, Phys. Rev. Lett. 95, 046601 (2005).
Joerg Wunderlich, Bernd Kaestner, Jairo Sinova, Tomas Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).
K. Nomura, Jairo Sinova, T. Jungwirth, Q. Niu, A. H. MacDonald, Phys. Rev. B 71, 041304(R) (2005).
E. M. Hankiewicz, L.W. Molenkamp, T. Jungwirth, and Jairo Sinova, Phys. Rev. B 70, 241301 (2004)
N. A. Sinitsyn, E. H. Hankiewicz, Winfried Teizer, Jairo Sinova, Phys. Rev. B 70, 081212 (R), (2004).
D. Culcer, Jairo Sinova, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Qian Niu, Phys. Rev. Lett 93, 046602 (2004).
Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004).
Anomalous Hall effect: where things
started, the unresolved problem
Spin-orbit coupling “force” deflects like-spin particles
majority
__ FSO
_
FSO
I
 H  R0 B  4πRs M
minority
V
Simple electrical measurement
of magnetization
InMnAs
controversial theoretically: three contributions to the AHE
(intrinsic deflection, skew scattering, side jump scattering)
Intrinsic deflection
Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY
because of the spin-orbit coupling in the periodic potential (electronics structure)
Movie created
by Mario
Borunda
Electrons have an “anomalous” velocity perpendicular to
the electric field related to their Berry’s phase curvature
which is nonzero when they have spin-orbit coupling.
Skew scattering
Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. This is also
known as Mott scattering used to polarize beams of particles in accelerators.
Movie created by Mario Borunda
Side-jump scattering
Electrons deflect first to one side due to the field created by the impurity and deflect back
when they leave the impurity since the field is opposite resulting in a side step.
Related to the intrinsic effect: analogy to refraction from an imbedded medium
Movie created by Mario Borunda
A history of controversy
(thanks to P. Bruno–
CESAM talk)
THE THREE CONTRIBUTIONS TO THE AHE:
MICROSCOPIC KUBO APPROACH
Skew scattering
n, q n’, k m, p
σHSkew
Skew
 (skew)-1 2~σ0 S
where
S = Q(k,p)/Q(p,k) – 1~
m, p
n, q
V0 Im[<k|q><q|p><p|k>]
Side-jump scattering
Vertex Corrections
 σIntrinsic
Intrinsic AHE: accelerating between scatterings
n, q
n’n, q
Intrinsic
σ0 /εF
FOCUS ON INTRINSIC AHE: semiclassical and Kubo
STRATEGY: compute this contribution in strongly SO coupled
ferromagnets and compare to experimental results, does it work?
n, q
Kubo:
Im
e
Re[ xy ]  
  f n'k  f nk 
V k n  n '
2


 

ˆ
ˆ
n' k vx nk nk v y n' k
( Enk  En 'k ) 2
n’n, q
Semiclassical approach in the “clean limit”

e2
Re[ xy ]   
f n 'k  n ( k )

V k n
K. Ohgushi, et al PRB 62, R6065 (2000); T.
Jungwirth et al PRL 88, 7208 (2002);
T. Jungwirth et al. Appl. Phys. Lett. 83, 320
(2003); M. Onoda et al J. Phys. Soc. Jpn.
71, 19 (2002); Z. Fang, et al, Science 302, 92
(2003).

Success of intrinsic AHE approach in comparing
to experiment: phenomenological “proof”
• DMS systems (Jungwirth et al PRL 2002, APL 03)
• Fe (Yao et al PRL 04)
• layered 2D ferromagnets such as SrRuO3 and pyrochlore
ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 71, 19
•
(2001),Taguchi et al., Science 291, 2573 (2001), Fang et al Science
302, 92 (2003), Shindou and Nagaosa, Phys. Rev. Lett. 87, 116801
(2001)]
colossal magnetoresistance of manganites, Ye et~al Phys.
Rev. Lett. 83, 3737 (1999).
Experiment
AH  1000 (
cm)-1
Theroy
AH  750 ( cm)-1
• CuCrSeBr compounts, Lee et al, Science 303, 1647 (2004)
Berry’s phase based AHE effect is quantitativesuccessful in many instances BUT still not a theory that
treats systematically intrinsic and extrinsic contribution
in an equal footing AND supposedly equivalent theories
give different results when disorder is incorporated.
Spin Hall effect
Take now a PARAMAGNET instead of a FERROMAGNET:
Spin-orbit coupling “force” deflects like-spin particles
_
FSO
__
FSO
non-magnetic
I
V=0
Carriers with same charge but opposite spin are deflected
by the spin-orbit coupling to opposite sides.
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection
Spin Hall Effect
(Dyaknov and Perel)
Interband
Coherent Response
Occupation #
Response
 (EF) 0
`Skew Scattering‘
(e2/h) kF (EF )1
X `Skewness’
Intrinsic
`Berry Phase’
(e2/h) kF

[Murakami et al,
Sinova et al]
[Hirsch, S.F. Zhang]
Influence of Disorder
`Side Jump’’
[Inoue et al, Misckenko et
al, Chalaev et al…]
Paramagnets
INTRINSIC SPIN-HALL EFFECT:
Murakami et al Science 2003 (cond-mat/0308167)
Sinova et al PRL 2004 (cont-mat/0307663)
as there is an intrinsic AHE (e.g. Diluted magnetic
semiconductors), there should be an intrinsic spin-Hall effect!!!
n, q
(differences: spin is a non-conserved quantity, define spin
current as the gradient term of the continuity equation.
Spin-Hall conductivity: linear response of this operator)
n’n, q
Inversion symmetry
 no R-SO
Broken inversion symmetry
 R-SO
2k 2
2k 2
 
Hk 
 0   (k xy  k y x ) 
 0    k
2m
2m
Bychkov and Rashba (1984)
‘Universal’ spin-Hall conductivity
n, q
n’n, q
 xysH
Color plot of spin-Hall conductivity:
yellow=e/8π and red=0
 e
m 2 2
*
 for n2 D  n2 D 
4
8




e n2 D
*

for
n

n
2D
2D
 8 n2* D
SHE conductivity: all contributions–
Kubo formalism perturbation theory
Skew
σ0 S
n, q
n’n, q
Intrinsic
σ0 /εF
Vertex Corrections
 σIntrinsic
= j = -e v
= jz = {v,sz}
Disorder effects: beyond the finite lifetime
approximation for Rashba 2DEG
Question: Are there any other major effects beyond the finite
life time broadening? Does side jump contribute significantly?
n, q
+…=0
+
n’n, q
For the Rashba example the side jump contribution cancels the intrinsic contribution!!
Inoue et al PRB 04
Raimondi et al PRB 04
Mishchenko et al PRL 04
Loss et al, PRB 05
Ladder partial sum vertex correction:
~
 
the vertex corrections are zero for 3D hole systems
(Murakami 04) and 2DHG (Bernevig and Zhang 05)
For these models one can do the exact calculations numerically:
testing the perturbation theory
k1 Rashba: g=constant α = 1
k3 Rashba: g=constant α = 3
Nomura et al. PRB 06
2DEG+Rahsba
2DHG+Rahsba
Numerical results for SHE conductivities
in 2D electrons and in 2D holes
Nomura et al PRB 05  
i

V

n,n '
Rashba model
2Dk^1
electron+Rashba
f ( E n )  f ( E n ' )  n | j  | n' n' | j | n
En  En'
E n  E n '  i
k^3 Rashba model
2D holes+Rashba
  6.4
Prediction: one should observe strong intrinsic SHE in 2D hole systems
OUTLINE


From electronics to spintronics:
 Electron multipersonality: using the charge and using the spin
 Success stories of metal based spintronics
 Why semiconductor spintronics may be better
 Spin-orbit coupling: the necessary evil
 The usual example: Das-Datta transistor
Spin-Hall effect:
 Normal and anomalous Hall effect and Spin Hall effect










Three contributions to the AHE
Turbulent history of the AHE
Recent focus on the intrinsic AHE
Application to the SHE
Short but turbulent history of the SHE
SHE experiments
Resolution of some of the controversy
Spin Hall spin accumulation
Theory challenges
Experimental challenges
First experimental observations at the end of 2004
Wunderlich, Kästner, Sinova, Jungwirth, cond-mat/0410295
PRL 05
1
Experimental observation of the spin-Hall effect in a two
dimensional spin-orbit coupled semiconductor system
Co-planar spin LED in GaAs 2D hole gas: ~1% polarization
Kato, Myars, Gossard, Awschalom, Science Nov 04
Observation of the spin Hall effect bulk in semiconductors
Local Kerr effect in n-type GaAs and InGaAs:
~0.03% polarization (weaker SO-coupling, stronger disorder)
CP [%]
0
-1
1.505
1.52
Light frequency (eV)
How our experiment worked: creating a spin-meter at edges
Conventional vertical spin-LED
Novel dual co-planar spin-LED
Y. Ohno: Nature 402, 790 (1999)
R. Fiederling: Nature 402, 787 (1999)
● SHE in 2DHG with strong and tunable SO
● SHE detected directly in the 2DHG
● Light emission near edge of the 2DHG
● No hetero-interface along the LED current
Top Emission
Electrod
e
QW
I
p-AlGaAs
Side Emission
etched
2DHG
i-GaAs
2DEG
n--doped AlGaAs
Spin polarization detected through circular polarization of emitted light
Experiment “A”
a
IP
-Ip
LED 1
p n
n
z
LED 2
zI
0
LED 1
y
x
x
Ip
x
z ILED 1
ILED 2
y
-1
-Ip
a
Experiment “B” +Ip
y
1
1
LED 1
0
LED 2
b
1.505
-1
1.510
1.515
1.520
E [eV]
Opposite perpendicular polarization for opposite Ip currents
or opposite edges  SPIN HALL EFFECT
CP [%]
1.5m
channel
+Ip
CP [%]
Ip
LED 1
OTHER RECENT EXPERIMENTS
Transport observation of the SHE by spin injection!!
Saitoh et al
APL 06
Sih et al, Nature 05, PRL 05
“demonstrate that the observed spin accumulation is due to a
transverse bulk electron spin current”
Valenzuela and
Tinkham condmat/0605423,
Nature 06
Next: solving some of the SHE controversy
• Does the SHE conductivity vanish due to scattering?
Seems to be the case in 2DRG+Rashba,
does not for any other system studied
• Dissipationless vs. dissipative transport
• Is the SHE non-zero in the mesoscopic regime?
• What is the best definition of spin-current to relate spin-conductivity to spin accumulation
•……
A COMMUNITY WILLING TO WORK TOGETHER
APCTP Workshop on Semiconductor
Nano-Spintronics: Spin-Hall Effect and Related Issues
August 8-11, 2005 APCTP, Pohang, Korea
http://faculty.physics.tamu.edu/sinova/SHE_workshop_APCTP_05.html
Semantics agreement:
The intrinsic contribution to the spin Hall conductivity is the spin Hall conductivity in the
limit of strong spin orbit coupling and >>1. This is equivalent to the single bubble
contribution to the Hall conductivity in the weakly scattering regime.
General agreement
•The spin Hall conductivity in a 2DEG with Rashba coupling vanishes in the absence of a magnetic
field and spin-dependent scattering. The intrinsic contribution to the spin Hall conductivity is
identically cancelled by scattering (even weak scattering). This unique feature of this model can be
traced back to the specific spin dynamics relating the rate of change of the spin and the spin
current directly induced, forcing such a spin current to vanish in a steady non-equilibrium situation.
•The cancellation observed in the 2DEG Rashba model is particular to this model and in general the
intrinsic and extrinsic contributions are non-zero in all the other models studied so far. In particular,
the vertex corrections to the spin-Hall conductivity vanish for p-doped models.
The new challenge: understanding spin accumulation
Spin is not conserved;
analogy with e-h system
Spin Accumulation – Weak SO
Quasi-equilibrium
Parallel conduction
Spin diffusion length
Burkov et al. PRB 70 (2004)
Spin Accumulation – Strong SO
?
Mean Free
Path?
Spin Precession
Length
SPIN ACCUMULATION IN 2DHG:
EXACT DIAGONALIZATION STUDIES
so>>ħ/
Width>>mean free path
Nomura, Wundrelich
et al PRB 06
Key length: spin precession length!!
Independent of  !!
n
p
1.5m
channel
LED1
0
y
-1
z
n LED2
x
1
0
-1
1.505
1.510
1.515
1.520
Energy in eV
Wunderlich, Kaestner, Sinova,
Jungwirth, Phys. Rev. Lett. '05
10m channel
- shows the basic SHE symmetries
- edge polarizations can be separated
over large distances with no significant
effect on the magnitude
- 1-2% polarization over detection
length of ~100nm consistent with
theory prediction (8% over 10nm
accumulation length)
Polarization in %
1
Nomura, Wunderlich, Sinova, Kaestner,
MacDonald, Jungwirth, Phys. Rev. B '05
Polarization in %
SHE experiment in
GaAs/AlGaAs 2DHG
WHERE WE ARE GOING (THEORY)
Theoretical achievements:
Intrinsic SHE
back to the beginning on a higher level
2003
Extrinsic SHE
approx microscopic modeling
Extrinsic + intrinsic AHE in graphene:
two approaches with the same answer
Theoretical challenges:
GUT the bulk (beyond simple graphene)
intrinsic + extrinsic SHE+AHE+AMR
Obtain the same results for different equivalent approaches
(Keldysh and Kubo must agree)
Others
materials and defects
coupling with the lattice
effects of interactions (spin Coulomb drag)
spin accumulation -> SHE conductivity
2006
WHERE WE ARE GOING (EXPERIMENTS)
Experimental achievements
Optical detection of current-induced polarization
photoluminescence (bulk and edge 2DHG)
Kerr/Faraday rotation (3D bulk and edge, 2DEG)
Transport detection of the SHE
Experimental (and experiment modeling) challenges:
General
edge electric field (Edelstein) vs. SHE induced spin accumulation
Photoluminescence cross section
edge electric field vs. SHE induced spin accumulation
free vs. defect bound recombination
spin accumulation vs. repopulation
angle-dependent luminescence (top vs. side emission)
hot electron theory of extrinsic experiments
SHE detection at finite frequencies
detection of the effect in the “clean” limit
Mario Borunda Sergio Rodriguez
Xin Liu
Alexey Kovalev Nikolai Sinitsyn
Texas A&M U. Texas A&M U.
Texas A&M U. Texas A&M U. Texas A&M U.
U. of Texas
Tomas Jungwirth
Inst. of Phys. ASCR
U. of Nottingham
Allan MacDonald
U of Texas
Joerg Wunderlich Laurens Molenkamp
Wuerzburg
Cambridge-Hitachi
Ewelina Hankiewicz
U. of Missouri
Texas A&M U.
Kentaro Nomura
U. Of Texas
Branislav Nikolic
U. of Delaware
Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo, Dimitri
Culcer , Qian Niu, S-Q Shen, Brian Gallagher, Tom Fox, Richard
Campton, Winfried Teizer, Artem Abanov
NERC
2D spin-LED
Spin-Hall effect measrement
Measurement of 2DHG
Rashba splitting
2DEG
2DHG
2DEG
VT
2DHG
VD
Light emitted comes from Type II recombination processes: 3D
electrons with 2D holes. 3D electrons have an asymmetric
momentum space population (e.g. ky>0)
Sub GaAs gap spectra analysis: EL vs PL
y
z
a
X:
bulk GaAs
excitons
B (A,C):
3D electron –
2D hole
recombination
EL
A
PL
2DHG
2DEG
I
4
B
A
X
GaAs/AlGaAs superlattice
GaAs substrate
E [eV]
2
b
p1 AlGaAs
8
Wafer 2 C
GaAs
0
A
B
-1
-2
0
-50
-100
z [nm]
-150
2
10
0
I
d
8
6
i-GaAs
n-AlGaAs
10
A
Int [a.u.]
I:
recombination
with impurity
states
c
GaAs
p-AlGaAs
etched
B Wafer 1
B
X
C
1.48 1.49 1.50 1.51 1.52
E [eV]
6
4
2
0
OUTLINE








Metal and semiconductor based spintronics
Spin-orbit coupling in semiconducting systems
Hall effect, Anomalous Hall effect, and Spin Hall effect
 Ordinary and quantum Hall effect
 Anomalous Hall effect and spin Hall effect (SHE)
 Intrinsic SHE in Rashba SO couple systems
Optical detection of the polarization
Our measuring technique: LED probe of polarization
 Lateral 2DEG-2DHG junction
 Comparison of electro-luminescence and photoluminescence
Measurement of the SO splitting: in-plane polarization
through asymmetric recombination
SHE measurement
Conclusions and outlook
Light polarization due to recombination with SO-split
hole-subband in a p-n LED under forward bias
Microscopic band-structure calculations of the 2DHG:
3D electron-2D hole
Recombination
0.50
a
0

20
+ 
HH+
0
0.25
<S>
E [meV]
20
spin-polarization of
HH+ and HH- subbands
<sz>HH<sx>HH+
0.00
<sx>HH-0.25
HH-
LH
-20
-0.2
ky
0.0
0,2
-0.50
[nm-1]
<sz>HH+
-0.2
0.0
0.2
ky [nm-1]
s=1/2 electrons to j=3/2 holes plus selection rules
 circular polarization of emitted light
spin operators of holes: j=3s
 in-plane polarization
10
x
0
detection
angle/polarization
z
z
α
-5
Bx = +3T
n
20 m
CP [%]
x, B
y
p
y
Bx = -3T
20
-10
Bz = -3T
10
Perp.-to plane
0
detection
angle/polarization
z, B
-10
x
y
-3 -2 -1 0 1 2 3
B [T]
Bz = +3T
1.500
1.505
-20
E [eV]
 NO perp.-to-plane component of polarization at B=0
 B≠0 behavior consistent with SO-split HH subband
Junction
5
In-plane