SPIN-HALL EFFECT
Download
1 / 53

SPIN-HALL EFFECT a new adventure in condensed matter physics - PowerPoint PPT Presentation


  • 115 Views
  • Uploaded on

SPIN-HALL EFFECT a new adventure in condensed matter physics. JAIRO SINOVA. San Houston State University, January 22 th 2008. Research fueled by:. NERC. Mario Borunda Texas A&M U. Sergio Rodriguez Texas A&M U. Xin Liu Texas A&M U. Alexey Kovalev Texas A&M U. Nikolai Sinitsyn

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' SPIN-HALL EFFECT a new adventure in condensed matter physics' - teresa


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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

Texas A&M U.

Sergio Rodriguez

Texas A&M U.

Xin Liu

Texas A&M U.

Alexey Kovalev

Texas A&M U.

Nikolai Sinitsyn

Texas A&M U.

U. of Texas

Ewelina Hankiewicz

U. of Missouri

Texas A&M U.

Laurens Molenkamp

Wuerzburg

Kentaro Nomura

U. Of Texas

Branislav Nikolic

U. of Delaware

Tomas Jungwirth

Inst. of Phys. ASCR

U. of Nottingham

Joerg Wunderlich

Cambridge-Hitachi

Allan MacDonald

U of Texas

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
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


Electronics

CHARGE

Two parts to his

personality !

SPIN

What is spintronics?

ELECTRONICS

Mr. Electron

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

Vg

>0

gate

S

D

-

-

-

-

-

-

thin free charge carrier

channel induced by electric field from gate

Using the charge

the field effect transistor:work horse of information processing

ALL computers have these

transistors in one form or another

insulator

semiconductor

substrate

HIGH tunablity of electronic transport

properties the key to FET success in

processing technology

High mobility 2DEG: IQHE, FQHE, MIT, etc.


Using the spin

ferromagnetism:work horse of information storing


1 st generation spintronic devices based on ferromagnetic metals gmr already in every computer

GMR allowed read-out heads in hard drives to be MUCH smaller

1st generation spintronic devices based on ferromagnetic metals: GMR– already in every computer

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

Produces

an electric field

Ingredients: -“Impurity” potential V(r)

- Motion of an electron

In the rest frame of an electron

the electric field generates and

effective magnetic field

This gives an effective interaction with the electron’s magnetic moment

Spin-orbit coupling interaction(one of the few echoes of relativistic physics in the solid state)

  • 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

Beff

Beff

Beff

-

-

-

v

v

v

Using SO: Datta-Das spin FET

V/2

V


Datta das spin fet the movie
Datta-Das spin FET: the movie

Movie created by Mario Borunda


Outline1
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

SPIN HALL EFFECTA 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).


majority

_

_

_

FSO

_

FSO

I

minority

V

Anomalous Hall effect: where things started, the unresolved problem

Spin-orbit coupling “force” deflects like-spin particles

Simple electrical measurement

of magnetization

InMnAs

controversial theoretically: three contributions to the AHE (intrinsic deflection, skew scattering, side jump scattering)


Intrinsic deflection
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
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
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

n’, k

n, q

m, p

m, p

n, q

n, q

n’n, q

THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH

Skew

σHSkew (skew)-1 2~σ0 S where

S = Q(k,p)/Q(p,k) – 1~

V0 Im[<k|q><q|p><p|k>]

Skew scattering

Side-jump scattering

Vertex Corrections

 σIntrinsic

Intrinsic AHE: accelerating between scatterings

Intrinsic

σ0 /εF


Focus on intrinsic ahe semiclassical and kubo

n, q

n’n, q

FOCUS ON INTRINSIC AHE: semiclassical and Kubo

STRATEGY: compute this contribution in strongly SO coupled ferromagnets and compare to experimental results, does it work?

Kubo:

Semiclassical approach in the “clean limit”

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
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).

  • CuCrSeBr compounts, Lee et al, Science 303, 1647 (2004)

Experiment

sAH  1000 (W cm)-1

Theroy

sAH  750 (W cm)-1

Berry’s phase based AHE effect is quantitative-successful 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.


_ experiment: phenomenological “proof”

_

_

FSO

_

non-magnetic

FSO

I

V=0

Spin Hall effect

Take now a PARAMAGNET instead of a FERROMAGNET: Spin-orbit coupling “force” deflects like-spin particles

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 experiment: phenomenological “proof”

(Dyaknov and Perel)

Interband

Coherent Response

 (EF) 0

  • Occupation #

  • Response

  • `Skew Scattering‘

  • (e2/h) kF (EF )1

    X `Skewness’

    [Hirsch, S.F. Zhang]

  • Intrinsic

  • `Berry Phase’

  • (e2/h) kF

    [Murakami et al, Sinova et al]

Influence of Disorder

`Side Jump’’

[Inoue et al, Misckenko et al, Chalaev et al…]

Paramagnets


n, experiment: phenomenological “proof”q

n’n, q

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!!!

(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)

Inversion symmetry

 no R-SO

Broken inversion symmetry

 R-SO

Bychkov and Rashba (1984)


Universal spin hall conductivity

n, experiment: phenomenological “proof”q

n’n, q

‘Universal’ spin-Hall conductivity

Color plot of spin-Hall conductivity:

yellow=e/8π and red=0


n, experiment: phenomenological “proof”q

n’n, q

= j = -e v

= jz = {v,sz}

SHE conductivity: all contributions– Kubo formalism perturbation theory

Skew

σ0 S

Intrinsic

σ0 /εF

Vertex Corrections

 σIntrinsic


Disorder effects beyond the finite lifetime approximation for rashba 2deg

n, experiment: phenomenological “proof”q

n’n, q

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?

+…=0

+

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

2DEG+Rahsba

2DHG+Rahsba

Nomura et al. PRB 06


Numerical results for she conductivities in 2d electrons and in 2d holes
Numerical results for SHE conductivities in 2D electrons and in 2D holes

Nomura et al PRB 05

k^1 Rashba model

k^3 Rashba model

2D electron+Rashba

2D holes+Rashba

Prediction: one should observe strong intrinsic SHE in 2D hole systems


Outline2
OUTLINE in 2D holes

  • 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 in 2D holesobservations at the end of 2004

Wunderlich, Kästner, Sinova, Jungwirth, cond-mat/0410295

PRL 05

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

CP [%]

1.505

1.52

Light frequency (eV)

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)


How our experiment worked: creating a spin-meter at edges in 2D holes

Conventionalvertical 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

2DHG

2DEG

Spin polarization detected through circular polarization of emitted light


Experiment “A” in 2D holes

LED 1

CP [%]

-Ip

a

Experiment “B”

+Ip

LED 1

CP [%]

LED 2

b

a

+Ip

E [eV]

Opposite perpendicular polarization for opposite Ip currents

or opposite edges  SPIN HALL EFFECT


OTHER RECENT EXPERIMENTS in 2D holes

Transport observation of the SHE by spin injection!!

Valenzuela and Tinkham cond-mat/0605423, Nature 06

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”


Next solving some of the she controversy
Next: solving some of the SHE controversy in 2D holes

  • 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 in 2D holes

APCTP Workshop on Semiconductor Nano-Spintronics: Spin-Hall Effect and Related IssuesAugust 8-11, 2005 APCTP, Pohang, Korea

http://faculty.physics.tamu.edu/sinova/SHE_workshop_APCTP_05.html


Semantics agreement: in 2D holesThe 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 in 2D holes

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 in 2D holes

?

Mean Free

Path?

Spin Precession

Length


SPIN ACCUMULATION IN 2DHG: EXACT DIAGONALIZATION STUDIES in 2D holes

so>>ħ/

Width>>mean free path

Nomura, Wundrelich et al PRB 06

Key length: spin precession length!!

Independent of  !!


n in 2D holes

LED

1

p

y

m

1.5

m

x

n

channel

LED

2

z

SHE experiment in GaAs/AlGaAs 2DHG

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)

Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05


WHERE WE ARE GOING (THEORY) in 2D holes

Theoretical achievements:

Intrinsic SHE

back to the beginning on a higher level

2003

2006

  • 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


WHERE WE ARE GOING (EXPERIMENTS) in 2D holes

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 in 2D holes

Texas A&M U.

Sergio Rodriguez

Texas A&M U.

Xin Liu

Texas A&M U.

Alexey Kovalev

Texas A&M U.

Nikolai Sinitsyn

Texas A&M U.

U. of Texas

Ewelina Hankiewicz

U. of Missouri

Texas A&M U.

Laurens Molenkamp

Wuerzburg

Kentaro Nomura

U. Of Texas

Branislav Nikolic

U. of Delaware

Tomas Jungwirth

Inst. of Phys. ASCR

U. of Nottingham

Joerg Wunderlich

Cambridge-Hitachi

Allan MacDonald

U of Texas

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


2DEG in 2D holes

VT

2DHG

2DEG

2DHG

VD

2D spin-LED

Spin-Hall effect measrement

Measurement of 2DHG Rashba splitting

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)


10 in 2D holes

c

B

Wafer 1

a

I

8

EL

A

PL

6

4

B

A

X

2

Int [a.u.]

0

10

I

d

b

8

p-

AlGaAs

C

Wafer 2

E [eV]

6

GaAs

A

4

B

X

2

B

C

A

0

z [nm]

1.48

1.49

1.50

1.51

1.52

E [eV]

Sub GaAs gap spectra analysis: EL vs PL

X :

bulk GaAs

excitons

I :

recombination

with impurity

states

B (A,C):

3D electron –

2D hole

recombination


Outline3
OUTLINE in 2D holes

  • 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 photo-luminescence

  • Measurement of the SO splitting: in-plane polarization through asymmetric recombination

  • SHE measurement

  • Conclusions and outlook


spin-polarization of in 2D holes

HH+ and HH- subbands

3D electron-2D hole

Recombination

20

a

<sz>HH-

0

+

-

<sx>HH+

E [meV]

HH+

<S>

<sx>HH-

HH-

LH

<sz>HH+

-0.2 0.0 0,2

ky [nm-1]

ky [nm-1]

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:

s=1/2 electrons to j=3/2 holes plus selection rules

 circular polarization of emitted light

spin operators of holes: j=3s

 in-planepolarization


p in 2D holes

p

y

y

x

x

n

n

Junction

Junction

z

z

m

m

20

20

m

m

In-plane

detection angle/polarization

Perp.-to plane

detection angle/polarization

 NO perp.-to-plane component of polarization at B=0

 B≠0 behavior consistent with SO-split HH subband


ad