1. POSTECH Physics Department Colloquium, 2018.03.21.
Ultrafast Optical Studies of Valley Pseudospin in Transition Metal Dichalcogenides -
Jonghwan Kim
Department of Materials Science and Engineering
POSTECH

2. Outline Valley Pseudospin State in TMD monolayers
Manipulation of Exciton Pseudospin
Relaxation of Electron Pseudospin
Diffusion Current of Pseudospin

3. Outline Valley Pseudospin State in TMD monolayers
Manipulation of Exciton Pseudospin
Relaxation of Electron Pseudospin
Diffusion Current of Pseudospin

4. Electronic Degree of Freedom
Spin
Charge

5. Valley Pseudospin Degree of Freedom
Example: Graphene A B
Time-reversal pair - - EF
Valley degree of freedom: Graphene as an example
Unique crystal structure: Honeycomb structure of carbon
Degeneracy in band structure: K and K’ point
Fermi level at Dirac point
Time-reversal pair
Binary degree of freedom: charge +/-, spin up/dn
Problem: How to distinguish
Equal probability at K and K’
Same charge (no way out)
No magnetic moment K -K
Physical control for valley pseudospin?
(Magnetic moment, Berry curvature, etc.)

6. Broken inversion symmetry
Access to Pseudospin
Origin of zero magnetic moment and Berry curvature: Symmetry A B
Broken inversion symmetry A B
*Orbital magnetic moment
𝜇 𝐾 = −𝜇 −𝐾 ≠0
Ω 𝐾 = −Ω −𝐾 ≠0
Time reversal symmetry :
𝜇 𝐾 = −𝜇 −𝐾
Breaking Inversion Symmetry in general causes multiple changes such as opening a gap.
Most importantly for valley: Magnetic moment
AB site symmetry breaking:
Conduction band
Valence band
Symmetric
Anti-symmetry band
Inversion symmetry :
𝜇 𝐾 = 𝜇 −𝐾
𝜇 𝐾 =0, 𝜇 −𝐾 =0
*Berry Curvature
Similarly,
Ω 𝐾 =0, Ω −𝐾 =0
PRL 99, (2007)

7. Valley Pseudospin in TMD Monolayer
MX2: M = Mo, W; X = S, Se
MoS2, MoSe2, WS2, WSe2
TMD monolayer
Introduction
Explicitly broken inversion symmetry
Band structure near Fermi level: Opened gap
Explicitly Broken Inversion Symmetry

8. Valley Pseudospin Electronic Structure
Berry Curvature of Valence Band K -K EF ↑ ↑
~ 450 meV ↑ ↑
TMD monolayer
Introduction
Explicitly broken inversion symmetry
Band structure near Fermi level: Opened gap
Chem. Soc. Rev., 2015, 44, 2643
Spin-Valley Locked Structure: Long spin/valley lifetime of holes!

9. Valley Pseudospin Electronic Structure
Valley degeneracy for quasiparticles in TMD monolayer K -K ↑ EF - - + +
TMD monolayer
Introduction
Explicitly broken inversion symmetry
Band structure near Fermi level: Opened gap
Electron, hole, exciton, and many more
Exciting Opportunity in valley-electronics and optoelectronics

10. Valley dependent magnetic moment
Valley Zeeman Effect
Valley dependent magnetic moment EF K -K
Under magnetic field
(Out-of-plane)
PRL 113, (2014)
Nature Physics 11, 141 (2015)
Nature Physics 11, 148 (2015)
PRL 114, (2015)
PRL 120, (2018)

11. Valley Dependent Berry Curvature
Valley Hall Effect
Valley Dependent Berry Curvature
Anomalous velocity:
Monolayer MoS2
𝑣 ⊥ =− 𝑒 ℏ 𝐸×Ω(𝑘)
F. Mak, et. al., Science 344, 1489 (2014)
J. Lee, et. al., Nature Nanotechnology 11, 421 (2016)
J. Lee, et. al., Nature Materials 16, 887 (2017)

12. Valley Pseudospin Dynamics? Lifetime Mobility Transient manipulation
Investigation with ultrafast optical spectroscopy!

13. Outline Valley Pseudospin State in TMD monolayers
Manipulation of Exciton Pseudospin
Relaxation of Electron Pseudospin
Diffusion Current of Pseudospin

14. Excitons in Atomically thin 2D crystals+ -
Coulomb
interaction
Exciton: Coulomb-bound e-h pairs
Strong Coulomb interaction
due to reduced dielectric screening
PRL 113, (2014)

15. Excitonic Energy Structure
Hydrogenic energy structure
Excitons in GaAs
Excitons in WSe2 monolayer
n=1 + -
n=2 + -
J. Luminescence 30, 154 (1985)
GaAs QW:
Binding energy < 10 meV
Atomically thin TMD:
Binding energy ~ Several 100 meV

16. Valley Pseudospin of Exciton
Light-matter interaction of exciton pseudospin
mj = +1
mj = -1
𝝈 +
𝝈 −
mj = 0 ↑
mj = 0 ↑ ↑ ↑ K -K
Helicity dependent optical selection rule ~ 𝜑 𝑐 𝑝 𝑥 ±𝑖 𝑝 𝑦 𝜑 𝑣 2
(C3 symmetry of atomic orbitals and Bloch phase winding)
Review: X. Xu, et. al., Nature Physics 10, 343 (2014)

17. Valley Pseudospin of Exciton
𝜑 𝑐 𝑝 𝑥 ±𝑖 𝑝 𝑦 𝜑 𝑣 2 : Helicity dependent light absorption and emission
𝜎 +
𝜎 + K -K
Generation and detection of pseudospin with ‘helicity of photon’
Review: X. Xu, et. al., Nature Physics 10, 343 (2014)

18. Quantum Coherent Manipulation of Pseudospin
Non-resonant dipole interaction: Optical Stark Effect
∣ 𝑏
∣ 𝑎+ℏ𝑤
𝐸0+𝛿
∣ 𝑏−ℏ𝑤
∣ 𝑎
Hybridization via dipole interaction ~ 𝑏 𝑝 𝑎 2
𝜹= 𝟐𝑺∙ 𝑬 𝒑 𝟐 ℏ𝜴
Below-resonance photon: Resonance energy blue shift

19. Valley-selective Optical Stark Effect
𝝈 +
Probe
𝝈 −
Probe
𝝈 +
Pump K -K
Exction resonance
Manipulation of information: Magnetic field
Large effective magnetic field 60T
Resonance energy blue shift: ~ 3 meV
J. Kim*, X. Hong*, et. al., Science 346, 1205 (2014)
also Gedik group at MIT

20. Valley-selective Optical Stark Effect
Ultrafast and efficient quantum coherent manipulation
Manipulation of information: Magnetic field
Large effective magnetic field 60T
Δ𝐸= 2𝑆∙ 𝐸 𝑝 2 ℏΩ
Optical Stark shift :
𝑩 𝒆𝒇𝒇 ~ 𝟔𝟎 𝑻
Δ𝐸=2 𝑔 𝑒𝑥 𝜇 𝐵 𝐵 𝑒𝑓𝑓 ( 𝑔 𝑒𝑥 ~ 1.5)
J. Kim*, X. Hong*, et. al., Science 346, 1205 (2014)

21. Outline Valley Pseudospin State in TMD monolayers
Manipulation of Exciton Pseudospin
Relaxation of Electron Pseudospin
Diffusion Current of Pseudospin

22. Valley Pseudospin Electronic Structure
Spin-Valley locked electronic structure
Path I
Spin flip and large momentum change ↑ ↑
∆𝐸 ~ 450 𝑚𝑒𝑉 ↑
Path II ↑
Large energy and large momentum change K -K
Possibly ultralong spin/valley lifetime!

23. Short Exciton Pseudospin Lifetime↑ ↑ K -K
Zhu et. al., Phys. Rev. B. 90, (2014)
Mei et. al., Nano Lett. 14, 202 (2014)
Exchange interaction of excitons: ~ psec
Maialle, Silva and Shan, Physical Review B 47, (1993)

24. Valley Pseudospin of Electrons
Resident carrier: Breaking exciton with defects
nsec valley lifetime ↑
Defect level ↑ K -K
Lifetime limited by defect and low valley polarization
L. Yang et. al., Nature Physics 11, 830 (2015)

25. ‘Ultrafast’ and ‘Intrinsic’ dynamic process for exciton dissociation?

26. Electronic Structure Engineering in vdW crystals
Indirect to direct gap transition
(MoS2)
Direct bandgap 1.7 – 0.3 eV
(Phosphorene)
Interlayer electron-phonon
Interaction (WSe2/hBN)
2 layer
1 layer
Bulk
vdW interaction in the crystals
Direct band gap to Indirect band gap transition
Size of direct band gap
Interlayer electron-phonon coupling
A. Splendiani, J. Kim et. al.
Nano Lett. 10, 1271 (2010)
L. Li*, J. Kim*, C. Jin* et. al,
Nature Nano 12, 21 (2016)
C. Jin*, J. Kim* et. al,
Nature Physics 13, 127 (2016)
Also, Fai Mak et. al. PRL (2010)

27. Carrier Dynamics Engineering in vdW Crystals
Ultrafast charge separation in TMD heterostructure
Charge transfer dynamics
Charge transfer time < 50 fs
X. Hong*, J. Kim*, S. Shi*, et. al., Nature Nanotechnology 9, 682 (2014)

28. Optical Generation of Pseudospin with Holes
WSe2
MoS2 + - K -K
WSe2 -
Pump +
J. Kim*, C. Jin*, et. al. Science Advances, 3:e (2017)

29. Optical Generation of Pseudospin with Holes
WSe2
MoS2 + - -
< 50 fs
MoS2
Probe + K -K
WSe2
J. Kim*, C. Jin*, et. al. Science Advances, 3:e (2017)

30. Heterostructure Device Few-layer graphene back gate
Graphene contact
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
TMD heterostructure
Few-layer graphene back gate

31. Relaxation of Pseudospin in Holes
Circular dichroism
Circular dichroism
1. Valley polarization: near unity (due to ultrafast exciton dissociation)
2. Valley lifetime: ~ usec (due to intrinsic process in ultraclean sample)
* Experiment at 10 Kelvin

32. Pseudospin Relaxation Mechanism
p+ − p- K -K
MoS2
p+ − p- = 0 means:
*Mention in all cases we pump exciton at K valley
Intervalley scattering: no total carrier density decay, but scatters to the other valley
Population relaxation: no intervalley scattering, but carriers decay K -K
1) Intervalley scattering:
2) Population relaxation: K -K

33. Pseudospin Relaxation Mechanism
Valley polarization K -K
MoS2
defect
Carrier density
Total density
Valley imbalance
If it is intervalley scattering
Intervalley scattering rate > 100 us
Population relaxation dominated
valley relaxation
Intervalley scattering rate can be much longer than microsecond

34. Outline Valley Pseudospin State in TMD monolayers
Manipulation of Exciton Pseudospin
Relaxation of Electron Pseudospin
Diffusion Current of Pseudospin

35. Mobility of Valley Pseudospin
Source
Optical excitation
( 𝜎 + )
∣ 𝐾
TMD heterostructure
Drain
Generation of Valley Pseudospin Current?

36. Space and Time-resolved Pseudospin Mapping
𝜏: time delay ∆x
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
pump, probe
~ 2 um width
Direct imaging of spin/pseudospin diffusion current in space and time
(Effectively transport experiment with microscopic spatial and ultrafast time resolution)
C. Jin*, J. Kim*, et. al. (Under review)

37. Space and Time-resolved Pseudospin Mapping
Local illumination at the edge
No Diffusion Current Captured.
C. Jin*, J. Kim*, et. al. (Under review)

38. Generation of Ultra Long Valley Pseudospin
Step 1
Ultrafast charge transfer
Step 2
Interlayer recombination
Step 3
Remanent Valley Polarization
Valley degree of freedom: Graphene as an example
Unique crystal structure: Honeycomb structure of carbon
Degeneracy in band structure: K and K’ point
Fermi level at Dirac point
Time-reversal pair
Binary degree of freedom: charge +/-, spin up/dn
Problem: How to distinguish
Equal probability at K and K’
Same charge (no way out)
No magnetic moment
C. Jin*, J. Kim*, et. al. (Under review)

39. Ultrafast charge transfer Step 2 Interlayer recombination Step 3
Remanent Valley Polarization
Valley degree of freedom: Graphene as an example
Unique crystal structure: Honeycomb structure of carbon
Degeneracy in band structure: K and K’ point
Fermi level at Dirac point
Time-reversal pair
Binary degree of freedom: charge +/-, spin up/dn
Problem: How to distinguish
Equal probability at K and K’
Same charge (no way out)
No magnetic moment
Long valley lifetime (only limited by intervalley scattering rate)
Near unity conversion from photoexcitation to valley carriers
Pure spin/valley polarization without charge carriers
Advantage:
C. Jin*, J. Kim*, et. al. (Under review)

40. Pure Spin-Valley Diffusion Current Image
Vertical linecuts
𝝉 = 0 ns
𝝉 = 400 ns
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
Valley diffusion current captured!
* measurement at 10 Kelvin
* hole doping: p0 = 1 x 1012 /cm2

41. Pure Spin-Valley Diffusion Current Image
Horizontal linecuts
∆x = 5 um
∆x = 0 um
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
Valley diffusion current captured!
* measurement at 10 Kelvin
* hole doping: p0 = 1 x 1012 /cm2

42. One-dimensional Diffusion-Decay Model
∆𝑝 𝑣 𝑥,𝑡 = Δ𝑝 𝜋(𝜎 𝐷𝑡) 𝑒 − 𝑥 2 𝜎 𝐷𝑡 𝑒 − 𝑡 𝜏
Experimental data
Simulated data
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
From simulation, D= 0.2 cm2/s, 𝝉 = 20 us, 𝒍 = 𝑫𝝉 = 20 um

43. High Spin-Valley Current Density
∆𝑝 𝑣 𝑥,𝑡 = Δ𝑝 𝜋(𝜎 𝐷𝑡) 𝑒 − 𝑥 2 𝜎 𝐷𝑡 𝑒 − 𝑡 𝜏
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
𝑗 𝑣 𝑥,𝑡 =−𝑞𝐷 𝜕Δ 𝑝 𝑣 𝑥,𝑡 𝜕𝑥
At optical excitation density 1012 /cm2:
Peak current density: 𝒋 𝒗 = 2 x 107 A/m2
Current: 𝑰 𝒗 = 0.2 uA (1 nm thickness, 10 um width)

44. Electrical Modulation of Diffusion Current
Gate-tunable Spin-Valley current
Heavier hole doping case
Hole doping case
Charge neutral case
p0 = 2.8 x 1012 /cm2
p0 = 1 x 1012 /cm2
p0 = ~ 0
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
D= 1.2 cm2/s
𝝉 = 2 us
D= 0.2 cm2/s
𝝉 = 20 us
D ~ 0
𝝉 = 0.4 us
𝒋 𝒗 = 1.2 x 108 A/m2
𝒋 𝒗 = 2 x 107 A/m2
𝒋 𝒗 ~ 0

45. Electrical Modulation of Diffusion Current
Gate-tunable spin-valley lifetime
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
electron concentration (1012/cm2)
(Neutral case and)
Electron-doping case: Limited by photoexcited carrier lifetime
Hole-doping case: Limited by intervalley scattering rate

46. Electrical Modulation of Diffusion Current
Gate-tunable diffusion constant (mobility)
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
Mobility is almost zero at low carrier concentration

47. Summary - TMD monolayer: Interesting system for many body physics
Valley-selective optical Stark effect
Ultrafast and efficient coherent control for
quantum state of valley pseudospin
WSe2
WS2 + - A
TMD heterostructure:
Excellent platform for Berry phase physics
Pure spin/valley diffusion current
1. Long valley lifetime: 20 us
2. Long valley diffusion length: 20 um
3. Large valley current density: 1.2 x 108 A/m2

48. Acknowledgement Advisor: Prof. Feng Wang Wang group
Arizona State Univ.
Prof. Sefaattin Tongay
Wang group
Chenhao Jin
M. Iqbal Bakti Utama
Emma C. Regan
Hans Kleemann (now in TU Dresden)
Xiaoping Hong (now in DJI)
Sufei Shi (now in RPI)
Zhiwen Shi (now in Shanghai jiao tong Univ.)
Peking Univ.
Prof. Yanfeng Zhang
National Institute for Materials Science
Dr. Kenji Watanabe
Dr. Takashi Taniguchi
Collaborations in Berkeley:
Prof. Alex Zettl
Prof. Junqiao Wu, Dr. Joonki Suh
Prof. Michael Crommie

49. Thank you for your attention!

50. Intervalley scattering rate Temperature dependence

51. Device Characterization
Band alignment and gate tuning
Optical reflection contrast
electron concentration (1012/cm2)
* Reason for valley relaxation:
1. Intervalley scattering: no total carrier density decay, but scatters to the other valley
2. Population relaxation: no intervalley scattering, but carriers decay
WSe2 exciton
WS2 exciton

52. Valley Information

53. Valley Information

54. Controlling Electronic Structure in vdW crystals
Graphene
Few-layer graphene
vdW heterostructure
Geim, Nature, 499, 419 (2013)