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

Feb 16, 2018 MPI-UBC-UT Winter School University of Tokyo on Quantum Materials Valleytronic Properties in 2D materials Yoshi Iwasa, Univ. Tokyo & RIKEN

Acknowledgements Univ Tokyo, Iwasa group 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)

Contents 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

2D Electron Systems n 2D (cm – 2 ) 10 11 10 9 10 ７ 10 13 10 15 insulator semiconductor metal He surface Interface Si MOS-FET (GaAs/AlGaAs ） http://phys.org/news/2011-02- https://en.wikipedia.org/wiki/2DEG http://www2.warwick.ac.uk/fac/sci/physics/current/... microwave-photons-nul...

2D Electron Systems → 2D Materials Interfaces 2D crystal Electrochemical (LAO/STO Interfaces FeSe/STO) Scotch Tape MBE electrolyte CVD

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

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

Direct gap in monolayer MoS 2 Direct gap ( ± K) Bulk 4-layer 2-layer Monolayer Indirect gap Normalized Splendiani et al., Nano Lett. (2010) Cao et al., Nat. Comm. (2012) Mak et al., Phys. Rev. Lett. (2010)

Transition Metal Dichalcogenides (TMD, MX 2 ) Graphene TMD 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)

Honeycomb lattice with broken inversion symmetry Graphene TMDs Massive Dirac fermion at ± K Massless Dirac fermion at ± K 0 𝛿 𝜐𝑟 𝑦 + 𝑗𝑟 𝑧 Δ 2 𝛿 𝜐𝑟 𝑦 + 𝑗𝑟 𝑧 𝐼 = 𝐼 = − 𝛿 𝜐𝑟 𝑦 − 𝑗𝑟 𝑧 0 𝛿 𝜐𝑟 𝑦 − 𝑗𝑟 𝑧 Δ 2

Valley dependent optical selection rules 𝑘 𝑨 = 1 ± 1 𝑘 𝑨 = 1 𝑘 𝑨 = −1 ∓ 1 2 𝑘 𝑨 = −1 2 𝑘 𝑨 = ± 1 𝑘 𝑨 = 0 𝑘 𝑨 = ∓ 1 2 𝑘 𝑨 = 0 2 Xiao et al. Phys. Rev. Lett. (2012) Large spin-orbit interaction Schematic of effective magnetic field

Circularly polarized Photoluminescence s - excitation  Excitation by circularly polarized laser  Selective detection of σ ± component s - s + 𝜃 = 𝐽 + − 𝐽 − 𝐽 + + 𝐽 − WSe Se 2 MoSe Se 2 MoS MoS 2 WS 2 WS Cao et al. , Nat. Comm. (2012) PL 63 % 5 % 56 % 42 % Zeng et al. , Nat. Nano. (2012) Mak et al. , Nat. Nano. (2012) Sallen et al. , Phys. Rev. B (2012)

Spin-valley locking Spin-resolved ARPES Broken inversion symmetry Spin-Orbit Interaction B eff p E int D. Xiao et al., PRL 108, 196802 (2012)

Monolayer vs. Bulk 1ML MoS 2 ( P6m2 ) 2H-MoS 2 ( P6 3 /mmc ) Bulk 3R-MoS 2 ( R3m ) S Mo S 3-fold 6-fold Noncentro- Centro- symmetric symmetric 3-fold Noncentrosymmetric K K’ K K’ Spin-Valley coupling in bulk

Spin-valley locking Spin-resolved ARPES Broken inversion symmetry Spin-Orbit Interaction B eff p E int D. Xiao et al., PRL 108, 196802 (2012) R. Suzuki et al., Nat Nano 9, 611 (2014). P. King’s group, Nat Phys 10, 385 (2014).

Progress of valleytronics in monolayer TMDs -K K • Circular dichroic PL H. Zeng et al., Nat Nano 7, 490 (2012). K. F. Mak et al., Nat Nano 7, 494 (2012). 𝝉 − 𝝉 + 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).

Be Berry curvature in mon onol olayer MoS oS2 ： wave vector ： Bloch function T. Cao et al. , Nat. Comm. 2, 887 (2012)

Hall effect ● Spontaneous Hall effect ● Hall effect External magnetic field Internal magnetic field ・ By external ・ WIthout ernal al magnetic fields al magnetic fields 18

Spontaneous Hall effect ● Various Hall effect ● Theory Anomalous velocity phonon electron / hole  1 E ( ) k 1     Ω k r ( ) r ( ) spin  k valley magnon Potential gradient e.g. electric fields E ・ optical response Be Berry curvatu ature re exciton on ・ composite particles internal magnetic field Hall effect of excitons ??? “Exciton with finite Berry curvature” W. Yao et al ., Phys. Rev. Lett. 101, 106401 (2008). S. I. Kuga et al ., Phys. Rev. B 78 78, 205201 (2008). Candidate ： Valley excitons in TMDs!! 19

Valley Hall Effect in TMD monolayer  1 ( ) k 1 E     Ω k r r ( ) ( )  k Potential gradient Berry curvat ature re e.g. electric fields E effective magnetic field J. Lee et al., K. F. Mak et al. Nature Nano 11, 421 (2016) Science 344, 1489 (2014)

Valley Hall effect in monolayer MoS2 Electrical detection of the optically excited electrons and holes  1 E ( ) k 1     Ω k r ( ) r ( )  k σ ＋ σ － K. F. Mak et al. Science 344, 1489 (2014)

Valley Hall effect in monolayer MoS2 Carrier doping by back gating Detection of the accumulated spins at the edge by Kerr rotation  1 E ( ) k 1     Ω k r r ( ) ( )  k J. Lee , K. F. Mak et al., Nature Nano 11, 421 (2016)

Valley Hall Effect in TMD monolayer  1 ( ) k 1 E     Ω k r r ( ) ( )  k Potential gradient Berry curvat ature re e.g. electric fields E effective magnetic field Theory of valley-Nernst effect J. Lee et al., K. F. Mak et al. S. Konabe et al. Nature Nano 11, 421 (2016) Science 344, 1489 (2014) PRB 90 , 075430 (2014).

Valley Hall Effect in TMD monolayer  1 ( ) k 1 E     Ω k r r ( ) ( )  k Potential gradient Berry curvat ature re e.g. electric fields E effective magnetic field Exciton Hall effect J. Lee et al., K. F. Mak et al. Nature Nano 11, 421 (2016) Science 344, 1489 (2014)

Exciton in monolayer TMDs ● Transition metal dichalcogenides Mo ・ Absorption spectrum E gap S excitonic states 200 meV K. F. Mak et al. , Nat. Mat. 12 12, 207 (2013). Z. Y. Zhu et al. , PRB 84 84, 153402 (2011). ・ two-dimensionality stable excitons ・ direct gap semiconductor 25

PL mapping in monolayer MoS 2

Obse servation on of of exc xciton on Ha Hall effect ● Polarization-resolved PL mapping （ Pumped by linear ed light ） arly ly polarized 1 m m (under B = 0 )

Obse servation on of of exc xciton on Ha Hall effect ● Polarization-resolved PL mapping （ Pumped by linear arized light ） arly y polar    I I I s  s  (under B = 0 ) -3 3

Trajector Tr ories s of of Ha Hall effect ● Color mapping of  I Conventional Hall effect 1 h e - 0 -1 Hall effect of excitons, visible objects. Tracing trajectories M. Onga et al., Nature Materials 16, 1193 (2017)

Hall angl Ha gle of of exc xciton on hall effect ● Definition & evaluation L     xy 0.20 0.02 EHE L xx Large Hall angle ( → real space observation) ● Sample dependence # 1 2 3  EHE 0.20 0.19 0.24 L xx    3 cf. 10 Valley Hall Effect L xy K. F. Mak et al., Science 344, 1489 (2014). ● Trion 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). ● Exciton Due to the Bose nature of exciton, the valley conductivity can be orders of magnitude larger than the Fermi one. T. Yu and M. W. Wu, PRB 93, 045414 (2016)

FE FET and nd EDLT (E (Electr ctric ic Dou oubl ble La Layer r Tra ransist nsistor or) Electric Double Layer Transistor (EDLT) FET 10 5 10 7 10 9 10 11 10 13 10 15 Insulator Semiconductor Metal Electronic phase transitions

TMD-EDLT S D Carrier density (WSe 2 ) FET vs EDLT (WSe 2 ) -5 -5 -5 15 10 10 10 220K EDLT -6 -6 -6 10 10 10 12 -7 -7 -7 2 ) 10 10 10 13 /cm 9 FET MoS 2 WSe 2 WSe 2 I DS (A) I DS (A) I DS (A) -8 -8 -8 10 10 10 n 2D (x10 6 -9 -9 -9 10 10 10 3 -10 -10 -10 10 10 10 0 -11 -11 -11 10 10 10 -4 -3 -2 -1 0 1 2 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 -100 -50 0 50 100 V G (V) V G (V) V G (V) V G (V) SiO 2 (Novoselov et al. , PNAS (2005)) HfO 2 ( Radsavljevic et al. , Nat. Nano. (2011) ) EDL ( Zhan ang et al. , Nano Lett. (2012) )