Optical Orientation and Spin Dynamics in Semiconductors€¦ · Optical Orientation and Spin Dynamics in Semiconductors Luyi Yang University of Toronto. Optics. Spin

Optical Orientation and Spin Dynamics in Semiconductors

Luyi YangUniversity of Toronto

Optics Spin

Outline• Optical orientation in conventional semiconductors

(e.g. GaAs, ZnSe, etc.)• Optical techniques for measuring spin properties

• Photoluminescence (exciton dynamics)• Time-resolved Faraday/Kerr rotation (resident

carriers & excitons)• Transient grating (transport properties)• Spin noise spectroscopy (resident carrier dynamics

in thermal equilibrium)






Typical values : GaAs Eg~1.52 eV, ∆so ∼0.34 eV (T = 4K)

III-V and II-VI Zinc-blende semiconductors

GaAs, ZnSe, etc.

Ga

As

J1/2

3/2

1/2

}

𝐽𝐽𝑧𝑧 = −32 +

32

−12 +

12

RCP LCP(3) (1) (3)(1)

Pump RCPSpin pol. = -50%=(1-3)/(1+3)

Pump LCPSpin pol. = +50%

Optical orientation in conventional semiconductors

𝐽𝐽𝑧𝑧 = −12

+12

Spin down Spin up

Typical values : GaAs Eg~1.52 eV, ∆so ∼0.34 eV (T = 4K)

In quantum confined structuresOptically induced spin polarization can be 100%

𝐽𝐽𝑧𝑧 = −32 +

32

−12 +

12

RCP LCP


+12

Spin down Spin up






How to detect the spin polarization? using again the optical selection rules of the interband transitions

𝐽𝐽𝑧𝑧 = −32 +

32

−12 +

12

RCP LCP(3) (1) (3)(1)


+12

Spin down Spin up

Pump w/RCP

Pump RCP, photoluminescence (PL) is also RCP

Light polarization:P0= (IRCP-ILCP)/(IRCP+ILCP)=25% (theory)

𝑃𝑃𝑐𝑐 =𝑃𝑃0

1 + 𝜏𝜏re𝜏𝜏𝑠𝑠

PL circular polarization

𝐽𝐽𝑧𝑧 = −32 +

32

−12 +

12

RCP LCP


+12

Quantum well

τs

τre τre

Pump w/RCP

P0 =100%

CB

HH

LH

𝑑𝑑𝑛𝑛↓𝑑𝑑𝑑𝑑 = 𝑔𝑔↓ −

𝑛𝑛↓𝜏𝜏re

−𝑛𝑛↓ − 𝑛𝑛↑𝜏𝜏𝑠𝑠

𝑔𝑔↓

𝑑𝑑𝑛𝑛↑𝑑𝑑𝑑𝑑 = −

𝑛𝑛↑𝜏𝜏re

−𝑛𝑛↑ − 𝑛𝑛↓𝜏𝜏𝑠𝑠

𝑑𝑑𝑛𝑛↓𝑑𝑑𝑑𝑑 =

𝑑𝑑𝑛𝑛↑𝑑𝑑𝑑𝑑 = 0Steady state:

𝑃𝑃𝑐𝑐 =𝑛𝑛↓ − 𝑛𝑛↑𝑛𝑛↓ + 𝑛𝑛↑

=1


𝑃𝑃𝑐𝑐 =𝑃𝑃0


Photoluminescence experiment

SpectrometerDetector

Sample

LinearPolarizer

QuarterWave plate

Filter

PL in

tens

ity

Circular Polarization

New physics: Coupled spin and valley quantum degrees of freedom in MX2

KK’

M (Mo, W), X (S, Se)

XM

Valley specific optical selection rules

• Polarized PL: Robust valley polarization (exciton effect)F. Wang, X. Xu, T. Heinz, etc.

Previous photoluminescence (PL) studies:

Mak et al., Nature Nanotech. 7, 494–498 (2012).

Pump (σ−)Pump σ−

Valley coherence >> PL lifetime

• TRPL studies: fast decay (1-100 ps): Exciton dynamics

Previous photoluminescence (PL) studies: Fast electron-hole recombination

C. Robert et al., Phys. Rev. B 93, 205423 (2016).

PL only measures exciton dynamicsCannot detect resident carriers

• Photoluminescence (PL): primarily exciton dynamics (70s)

• Time-resolved Faraday/Kerr rotation: background carrier (& exciton) dynamics (90s)Pump

I+(-)

PL lifetime: 1 ns in GaAs

Spin coherence time: 100 ns in n-GaAs>> exciton lifetime (1ns)

(in equilibrium)µ

n-type

kΓ

E




carriers & excitons)• Transient grating (spin propagation)• Spin noise spectroscopy (resident carrier dynamics


Kerr rotation

M θK

Optical Faraday/ Kerr rotation:θF/K ~ (nRCP-nLCP)

~ (αRCP-αLCP)

kΓ

E

θK~ (n↑ - n↓) Measure electron polarization, long after holes are gone

Kerr rotation spectroscopy: A direct probe of the resident carrier polarization

Ener

gy

Absorption

RCP LCP

0

αRCPαLCP

Index of refraction0

nRCPnLCP

0 0

Time-resolved Faraday/Kerr rotation experiment

Pump

Time delay

Fara

day

rota

tion

θF

Pump

ProbeKikkawa and Awschalom, Science 277, 1284 (1997).

Spin coherence in conventional semiconductors

Exciton lifetime: 100 ps

Electron spin coherence time: a few ns(& no holes)

n-ZnSe QW

Extremely long decay of resident carriers in TMDs (tomorrow’s talk)

Nanosecond – microsecond decay >> PL lifetime (1-100 ps)






Pump 1 Pump 2

Parallel polarization Intensity grating e-h density wave

Orthogonal polarization Helicity grating Spin density wave

Measuring charge & spin dynamics in q-spaceCreate transient grating of charge or spin

Position

1 micron

Tune q by changing the angle between the interfering beams.

Measuring spin dynamics in q-spaceCreate transient spin grating

Photoinduced transient gratings

Probe beam

Amplitude of diffracted beam

Time delay

Probing the grating decay

which has solutions of the form:

where,

Diffusion with loss term

q2Γ q

Low q High q

1/τs

Normal diffusion

Electron-hole diffusion in n-GaAs QW

Yang et al., PRL 106, 247401 (2011).

Spin diffusion in n-GaAs QW

Yang, et al., Nature Physics 8, 153 (2012).

=

Ohmic contacts

2DEG

e flow

Current-driven spin texture

Doppler velocimetrymoving grating Doppler shifts the diffracted probe

[Amp.] [phase]xDensity wave =)(ω

)(ω

)( φω +

Diffusion,lifetimes

mobilitygrating

Temporal resolution: ~100 fsSpatial resolution: ~1 nm

Yang et al., PRL 106, 247401 (2011). Yang et al., Nature Physics 8, 153 (2012).

�̇�𝜙 𝑞𝑞 = 𝑣𝑣𝑑𝑑𝑞𝑞

Electron-hole drift in n-GaAs QW

Yang et al., PRL 106, 247401 (2011).

�̇�𝜙 𝑞𝑞 = 𝑣𝑣𝑑𝑑𝑞𝑞�̇�𝜙 𝑞𝑞 𝑑𝑑

Spin drift in n-GaAs QW�̇�𝜙− 𝑞𝑞 ~𝑣𝑣𝑑𝑑(𝑞𝑞 − 𝑞𝑞0)

𝜇𝜇𝑠𝑠 = 𝑣𝑣𝑑𝑑/𝐸𝐸

Yang, et al., Nature Physics 8, 153 (2012).






Traditional way to probe spin dynamics

However, the fluctuation-dissipation theorem says one can measure the dynamics in thermal equilibrium via intrinsic fluctuations.

z

Pump-probe, ESR, NMR

Johnson noise

Spin noise spectroscopy

Atomic gases: Nature 431, 49 (2004). Semiconductors: PRB 79, 035208 (2009).QDs: PRL 104, 036601 (2010), PRL 108, 186603 (2012).

zMeasure the intrinsic and random spin fluctuations in thermal equilibrium.

Bulk n-GaAs

Spin noise experiment in n-GaAs

Spin lifetime, g-factor, etc.

SummaryPL

inte

nsity

Circular Polarization

Optical Orientation and Spin Dynamics in Semiconductors€¦ · Optical Orientation and Spin Dynamics in Semiconductors Luyi Yang University of Toronto. Optics. Spin

Documents