Valleytronic Properties in 2D materials Yoshi Iwasa, Univ. Tokyo - - PowerPoint PPT Presentation

SLIDE 1

Valleytronic Properties in 2D materials

Yoshi Iwasa, Univ. Tokyo & RIKEN

MPI-UBC-UT Winter School

• n Quantum Materials

Feb 16, 2018 University of Tokyo

SLIDE 2

SARPES M. Sakano, K. Ishizaka (Tokyo), S. Shin, K. Yaji (ISSP), K. Miyamoto, T. Okuda (Hiroshima) High magnetic field measurements Y. Kohama, M. Tokunaga (ISSP) Theory T. Oka (Dresden), M. S. Bahramy (Tokyo), Y. Yanase、Y. Nakamura (Kyoto)

Acknowledgements

Univ Tokyo, Iwasa group

SLIDE 3

• 1. Introduction
• 2D materials
• Valley degree of freedom in TMDs
• 2. Valleytronics
• Valley Hall effect
• Circularly polarized light source
• 3. Superconductivity with spin-valley locking
• Enhanced Hc2 by SOI

Contents

SLIDE 4

n2D (cm–2)

109 1011 1013 1015 10７

semiconductor insulator Si MOS-FET metal Interface (GaAs/AlGaAs） He surface

2D Electron Systems

http://www2.warwick.ac.uk/fac/sci/physics/current/... https://en.wikipedia.org/wiki/2DEG http://phys.org/news/2011-02- microwave-photons-nul...

SLIDE 5

Electrochemical Interfaces 2D crystal Interfaces (LAO/STO FeSe/STO)

2D Electron Systems → 2D Materials

Scotch Tape CVD MBE electrolyte

SLIDE 6

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2) M: Mo, W, Ta, … X:S, Se, Te 7.2 eV (indirect) 0.6~2.3 eV depending on # of layers ~2 eV (monolayer) ~0.3 eV (bulk) Black Phosphorus Graphene 0 eV h-BN

SLIDE 7

Valleytronics

Valley: as information carriers Candidate materials: Si Diamond, AlAs Bi graphene Challenge: Search for valley selective external perturbation

SLIDE 8

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al., Nano Lett. (2010)

4-layer 2-layer

Cao et al., Nat. Comm. (2012) Mak et al., Phys. Rev. Lett. (2010)

Normalized

Direct gap (±K) Indirect gap

SLIDE 9

Transition Metal Dichalcogenides (TMD, MX2)

Monolayer Isolation (PNAS 2005) Photoluminescence (PRL 2010) Monolayer FET(NNano 2011) Valleytronics (NNano 2012) Superconductivity (Science 2012) Photodetectors (NNano 2013) Light Emitting Diodes (Science 2014) Piezoelectic (Nature 2014) Laser (Nature 2015) Thermolelectrics (2015)

Graphene TMD

SLIDE 10

Honeycomb lattice with broken inversion symmetry

Graphene TMDs Massless Dirac fermion at ±K Massive Dirac fermion at ±K

𝐼 = 𝛿 𝜐𝑟𝑦 + 𝑗𝑟𝑧 𝛿 𝜐𝑟𝑦 − 𝑗𝑟𝑧 𝐼 = Δ 2 𝛿 𝜐𝑟𝑦 + 𝑗𝑟𝑧 𝛿 𝜐𝑟𝑦 − 𝑗𝑟𝑧 − Δ 2

SLIDE 11

Valley dependent optical selection rules

𝑘𝑨 = 0 𝑘𝑨 = 0 𝑘𝑨 = 1 𝑘𝑨 = −1

Large spin-orbit interaction

𝑘𝑨 = ∓ 1 2 𝑘𝑨 = ± 1 2 𝑘𝑨 = 1 ± 1 2 𝑘𝑨 = −1 ∓ 1 2

Schematic of effective magnetic field

Xiao et al. Phys. Rev. Lett. (2012)

SLIDE 12

Circularly polarized Photoluminescence

Cao et al., Nat. Comm. (2012) Zeng et al., Nat. Nano. (2012) Mak et al., Nat. Nano. (2012) Sallen et al., Phys. Rev. B (2012)

WSe Se2 MoSe Se2 MoS MoS2 WS WS2 PL 63 % 5 % 56 % 42 %

• Excitation by circularly polarized laser
• Selective detection of σ± component

𝜃 = 𝐽+ − 𝐽− 𝐽+ + 𝐽−

s+ s-

s- excitation

SLIDE 13

Spin-valley locking

• D. Xiao et al., PRL 108, 196802 (2012)

Eint Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

Spin-resolved ARPES

SLIDE 14

1ML MoS2 (P6m2)

Mo S

Noncentro- symmetric K K’ 2H-MoS2 (P63 /mmc) Centro- symmetric

6-fold

K K’

S 3-fold

Bulk 3R-MoS2(R3m) Noncentrosymmetric

Spin-Valley coupling in bulk

3-fold

Monolayer vs. Bulk

SLIDE 15

Spin-valley locking

• R. Suzuki et al., Nat Nano 9, 611 (2014).

Spin-resolved ARPES

• D. Xiao et al., PRL 108, 196802 (2012)

Eint Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

• P. King’s group, Nat Phys 10, 385 (2014).

SLIDE 16

Progress of valleytronics in monolayer TMDs

• Circular dichroic PL
• H. Zeng et al., Nat Nano 7, 490 (2012).
• K. F. Mak et al., Nat Nano 7, 494 (2012).
• T. Cao et al., Nat. Comm. 3, 887 (2012).
• EO conversion

(valley light emitting transistor)

• Y. J. Zhang et al., Science 344, 725 (2014).
• OE conversion

(valley Hall effect)

• K. F. Mak et al. Science 344, 1489 (2014).
• J. Lee et al., Nat Nano 11, 421 (2016).
• Magneto-optics (valley Zeeman effect)
• L. Li et al., PRL 113, 266804 (2014).
• D. MacNeil et al., PRL 114, 037401 (2015).
• A. Srivastava et al., Nat Phys 11, 141 (2015).
• G. Aivasian et al., Nat Phys 11, 148 (2015).

𝝉+ 𝝉−

• K

K

SLIDE 17

：wave vector ：Bloch function

Be Berry curvature in mon

• nol
• layer MoS
• S2
• T. Cao et al., Nat. Comm. 2, 887 (2012)

SLIDE 18

18

• Hall effect

・By external al magnetic fields External magnetic field

• Spontaneous Hall effect

Internal magnetic field ・WIthout ernal al magnetic fields

Hall effect

SLIDE 19

19

spin magnon phonon electron / hole valley

exciton

• n

・optical response ・composite particles Hall effect of excitons ???

1 ( ) 1 ( ) ( ) E       k r r Ω k k

Anomalous velocity

Be Berry curvatu ature re

Potential gradient e.g. electric fields E internal magnetic field “Exciton with finite Berry curvature” Valley excitons in TMDs!! Candidate：

• Various Hall effect
• Theory
• W. Yao et al., Phys. Rev. Lett. 101, 106401 (2008).
• S. I. Kuga et al., Phys. Rev. B 78

78, 205201 (2008).

Spontaneous Hall effect

SLIDE 20

• K. F. Mak et al.

Science 344, 1489 (2014)

• J. Lee et al.,

Nature Nano 11, 421 (2016)

Berry curvat ature re

Potential gradient e.g. electric fields E effective magnetic field

1 ( ) 1 ( ) ( ) E       k r r Ω k k

Valley Hall Effect in TMD monolayer

SLIDE 21

Valley Hall effect in monolayer MoS2

1 ( ) 1 ( ) ( ) E       k r r Ω k k

• K. F. Mak et al.

Science 344, 1489 (2014)

Electrical detection of the optically excited electrons and holes

σ

＋

σ

－

SLIDE 22

Valley Hall effect in monolayer MoS2

• J. Lee , K. F. Mak et al., Nature Nano 11, 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation Carrier doping by back gating

1 ( ) 1 ( ) ( ) E       k r r Ω k k

SLIDE 23

• K. F. Mak et al.

Science 344, 1489 (2014)

• J. Lee et al.,

Nature Nano 11, 421 (2016)

Berry curvat ature re

Potential gradient e.g. electric fields E effective magnetic field

1 ( ) 1 ( ) ( ) E       k r r Ω k k

• S. Konabe et al.

PRB 90, 075430 (2014).

Theory of valley-Nernst effect

Valley Hall Effect in TMD monolayer

SLIDE 24

Exciton Hall effect

• K. F. Mak et al.

Science 344, 1489 (2014)

• J. Lee et al.,

Nature Nano 11, 421 (2016)

Berry curvat ature re

Potential gradient e.g. electric fields E effective magnetic field

1 ( ) 1 ( ) ( ) E       k r r Ω k k

Valley Hall Effect in TMD monolayer

SLIDE 25

25

Mo S

• Z. Y. Zhu et al., PRB 84

84, 153402 (2011).

Egap excitonic states ・Absorption spectrum 200 meV

• K. F. Mak et al., Nat. Mat. 12

12, 207 (2013).

stable excitons

Exciton in monolayer TMDs

・ two-dimensionality ・ direct gap semiconductor

• Transition metal dichalcogenides

SLIDE 26

PL mapping in monolayer MoS2

SLIDE 27

1 mm

Obse servation

• n of
• f exc

xciton

• n Ha

Hall effect

• Polarization-resolved PL mapping（Pumped by linear

arly ly polarized ed light）

(under B = 0 )

SLIDE 28

I I I

s s  

  

(under B = 0 )

• 3

3

• Polarization-resolved PL mapping（Pumped by linear

arly y polar arized light）

Obse servation

• n of
• f exc

xciton

• n Ha

Hall effect

SLIDE 29

• Color mapping of I

Hall effect of excitons, visible objects. Tracing trajectories

1

• 1

Conventional Hall effect

h e-

Tr Trajector

• ries

s of

• f Ha

Hall effect

• M. Onga et al., Nature Materials 16, 1193 (2017)

SLIDE 30

• Definition & evaluation

xx

L

xy

L

3 Valley Hall Effect

10 





cf.

• K. F. Mak et al., Science 344, 1489 (2014).

EHE

0.20 0.02

xy xx

L L    

Large Hall angle (→ real space observation)

• Sample dependence

# 1 2 3 EHE 0.20 0.19 0.24

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction).

• H. Yu et al., Nat. Comm. 5, 3876 (2014).

Ha Hall angl gle of

• f exc

xciton

• n hall effect
• Trion
• Exciton

Due to the Bose nature of exciton, the valley conductivity can be orders

• f magnitude larger than the Fermi one.
• T. Yu and M. W. Wu, PRB 93, 045414 (2016)

SLIDE 31

107 109 1011 1013 1015 105

Semiconductor Metal Electronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FE FET and nd EDLT (E (Electr ctric ic Dou

• ubl

ble La Layer r Tra ransist nsistor

• r)

SLIDE 32

TMD-EDLT

FET vs EDLT (WSe2)

10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

IDS (A)

• 100
• 50

50 100 VG (V) FET EDLT

Carrier density (WSe2)

220K

15 12 9 6 3 n2D (x10

13 /cm 2)

• 4
• 3
• 2
• 1

1 2 VG (V)

10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

IDS (A)

• 4
• 3
• 2
• 1

1 2 VG (V) WSe2 10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

IDS (A)

• 4
• 3
• 2
• 1

1 2 VG (V) WSe2 MoS2

SiO2 (Novoselov et al., PNAS (2005)) HfO2 (Radsavljevic et al., Nat. Nano. (2011)) EDL (Zhan ang et al., Nano Lett. (2012)) S D

SLIDE 33

Field-induced p-i-n Junction

40 30 20 10 IDS (mA) 2.0 1.5 1.0 0.5 0.0 V4T (V) 4 3 2 1 VDS (V) VG = 2 V

Output curve

40 30 20 10 IDS (mA) 2.0 1.5 1.0 0.5 0.0 V4T (V) 4 3 2 1 VDS (V) VG = 2 V 40 30 20 10 IDS (mA) 2.0 1.5 1.0 0.5 0.0 V4T (V) 4 3 2 1 VDS (V) VG = 2 V 40 30 20 10 IDS (mA) 4 3 2 1 VDS (V) VG = 2 V Cool down here S D V V V

SLIDE 34

20 15 10 5 IDS (mA) 3 2 1

• 1
• 2
• 3

VDS (V) 220 K 150 K

Field-induced p-i-n Junction

RH2 RH1

• 500

500 RH1 ()

• 6
• 3

3 6 B (T) 500

• 500

RH2 ()

• 6
• 3

3 6 B (T)

Hall effect measurement

2.2 × 1013/cm2 −1.5 × 1013/cm2

Output curve Zhang et al., Nano Lett. (2013)

SLIDE 35

Electroluminescence from WSe2

2V 3V 4V 5V 6V Bias

24 18 12 6 EL intensity (a.u.) 15 10 5 Bias current (mA)

100 K

Absorption PL intensity EL intensity 2.2 2.0 1.8 1.6 Photon energy (eV) excitation 2.33 eV

A-exciton B-exciton He et al., PRL (2014) 100 K RT RT

5 μm Au/Ti

• Y. J. Zhang et al., Science 344, 725 (2014)

SLIDE 36

Electroluminescence from WSe2

SiN gating: Pospischil et al. Nat. Nano. (2014) hBN gating: Ross et al. Nat. Nano. (2014) HfO2 gating: Baugher et al. Nat. Nano. (2014)

Simultaneous publications

Current-induced circularly polarized EL

EL intensity (a.u.) 1.65 1.55 1.45 Photon energy (eV) s- s+ EDL gating

• Y. J. Zhang et al. Science (2014)

40 K

SLIDE 37

Electronic structure of gated multilayer MoS2

z Real space (SC state) Quas asi-monolay ayer SC n(z)

• M. S. Bahramy

E

+ + + + +

• T. Brumme et al. .
• Phys. Rev. B 91, 155436 (2015)

Gated multilayer is a mimic of monolayer

• H. T. Yuan et al., Nat Phys (2013)

SLIDE 38

Electrical Control of Circular Polarization

WSe2 170 K

Field-effect doping is reversible and tunable Modulation of diode profile

Circularly polarized light source showing electrical controllability

• Y. J. Zhang et al. Science (2014)

SLIDE 39

Circularly Polarized EL from MoSe2

• M. Onga, et al. APL (2016).

MoSe2 170 K

EL intensity (a.u.) 1.60 1.55 1.50 1.45 Photon energy (eV)

6 K

SLIDE 40

Helical Light Generation

Yang et al., Adv. Mater. (2013) http://www.ptt.ruhr-uni-bochum.de/

Structure Angular momentum selection rule

Helicity control needs spin (External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current (External in-plane electric field)

Optical filter

Konishi et al., PRL. (2011)

SLIDE 41

• J. T. Ye et al. Science 338, 1193 (2012)

10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K) 10

2

10

3

10

4

10

5

10

6

10

7

Rs () 100 80 60 40 20 T (K)

VEDLT=0V VEDLT=6V

Gate induced superconductivity in MoS2

SLIDE 42

Newly emerging 2D superconductors

MBE (layer-by-layer growth) Pb, In single layer (1L)

Nature Phys. 6, 104 (2010). PRL 107 107, 207001 (2011).

FeSe-1L

CPL 29 29, 03742 (2012).

Heavy Fermion superlattice CVD Mo2C-1～2L

Nature Mat. 14 14, 1135 (2015).

Ionic gating (EDLT) ZrNCl-quasi-1L

Nature Mat. 9, 1314 (2010). Science 350 350, 409 (2015).

TMDCs-quasi-1L

Science 338 338, 1193 (2012).

• Sci. Rep. 5, 12534 (2015).

Nature Nano. 11 11, 339 (2016). Nature Phys. 12 12, 144 (2016).

mechanically-exfoliated (2D crystals) BSCCO-1L

Nature Comm. 5, 5708 (2014).

NbSe2-1L

Nano Letter 15 15, 4914 (2015). Nature Nanotech. 10 10, 765 (2015).

intercalated graphene

STO & KTO Cuprate (LSCO)

Nature Mat 7, 855 (2008). Nature Nano. 6, 408 (2011). Nature 472 472, 458 (2011). PNAS 112 112, 11795 (2015). ACS Nano 10 10, 2761 (2016). Nature Phys. 7, 849 (2011).

Tl-Pb single layer (1L)

PRL 115 115, 147003 (2015).

SLIDE 43

2D superconductors

• Y. Saito et al. Nature Reviews Materials 2, 16094 (2016)

SLIDE 44

EDLT: New platform of 2D superconductivity

Enhan anced Hc2 b by y SOI

Saito, Nat Phys (2016)

Nonreciprocal al Supercurrent

Wakatsuki/Saito, Sci Adv (2017) Qin, Nat Comm (2017)

Quan antum Phas ase Tran ansition

Saito, Science (2015), Nat Comm (2018)

(weak pinning) (broken inversion symmetry) (materials)

SrTiO3, KTaO3, LSCO, YBCO ZrNCl, MoS2, MoSe2, TiSe2, FeSe, …

SLIDE 45

Noncentrosymmetric superconductors

1 2

2 2 



P c

• rb

c

H H 

Parity mixture Benchmark; Enhanced Pauli limit

P c

H 2

To observe Pauli limit, Maki parameter

Rashba-type spin polarization

Heavy electron mass Reduced dimensions Two ways CePt3Si CeRhSi3, CeIrSi3, Uir, Li2Pt3B, Li2Pd3B,・・・・

SLIDE 46

Monolayer MoS2; a new class of noncentrosymmetric SC

2H-type structure z

Trigonal structure with simple band structure with out-of-plane spin polarization Quas asi-monolay ayer SC n(z)

E

+ + + + +

DFT calculation~ 1 layer

Brumme et al., PRB 91, 155436 (2015).

SLIDE 47

R-T Curves for H and H// (MoS2)

H H

q c H

SLIDE 48

20 15 10 5

Bc2 (T)

10.0 5.0 0.0

T (K)

dSC  1.4 nm GL(0)  8.1 nm

Pau auli limit

H

2 / 1 // 2 2 2

) / 1 ( ) ( 2 12 ) ( ) / 1 ( ) ( 2 ) (

c sc GL c c GL c

T T d T H T T T H      



 

(0 = h/2e) 2D Tinkam model

H

+ + +

Thickness of superconductivity in MoS2-EDLT

• Cf. EDA → monolayer
• T. Brumme et al., PRB91, 155436 (2015).

SLIDE 49

High field measurement at ISSP, Univ Tokyo on gated MoS2

Experime riment nt

conventional Pauli limit

H

2D GL (orbital limit) Enhan anced Pau auli limit

• Y. Saito et al., Nature Physics 12, 144 (2016).

SLIDE 50

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

• M. S. Bahramy

s + f symmetry FFLO Intervalley pairing

SLIDE 51

Comparison with Theory for MoS2

Hc2 : semiquantitatively explained by Zeeman type spin-valley locking

Experime riment nt Theory ry (Paul uli i limit)

Rashba Zeeman

conventional Pauli limit

H

2D GL (orbital limit) Enhanced Pau auli limit

• M. S. Bahramy
• Y. Nakamura and Y. Yanase
• Y. Saito et al. Nature Phys. 12, 144 (2016)
• J. M. Lu et al. Science. 350, 1353 (2015)
• X. Xi et al. Nature Phys. 12, 139 (2016)

Further theory Ilic et al.. PRL 119, 117001 117001 (2017)

SLIDE 52

Summary: Valleytronic Properties of 2D materials

• 1. Introduction
• 2. Exciton Hall effect
• 3. Valley Light Emitting Transistor
• 4. 2D superconductivity
• Enhanced Hc2 by SOI