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)

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

𝐽𝐽𝑧𝑧 = −12

+12

Spin down Spin up

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)

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)

𝐽𝐽𝑧𝑧 = −12

+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

𝐽𝐽𝑧𝑧 = −12

+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

1 + 𝜏𝜏re𝜏𝜏𝑠𝑠

𝑃𝑃𝑐𝑐 =𝑃𝑃0

1 + 𝜏𝜏re𝜏𝜏𝑠𝑠

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

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 (spin propagation)• Spin noise spectroscopy (resident carrier dynamics

in thermal equilibrium)

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)

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)

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).

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)

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