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