Valleytronic Properties in 2D materials

Transcription

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

2 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)

3 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

4 2D Electron Systems insulator semiconductor metal n 2D (cm 2 ) He surface Interface (GaAs/AlGaAs) Si MOS-FET microwave-photons-nul

5 2D Electron Systems 2D Materials 2D crystal Interfaces (LAO/STO FeSe/STO) Electrochemical Interfaces Scotch Tape MBE electrolyte CVD

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

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

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

9 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)

10 Honeycomb lattice with broken inversion symmetry Graphene TMDs Massless Dirac fermion at ±K Massive Dirac fermion at ±K H = 0 γ τq x + iq y γ τq x iq y 0 H = Δ 2 γ τq x + iq y γ τq x iq y Δ 2

11 Valley dependent optical selection rules j z j z = 11± 1 j z j= z = j z j z = j z j z = ± Xiao et al. Phys. Rev. Lett. (2012) Large spin-orbit interaction Schematic of effective magnetic field

12 Circularly polarized Photoluminescence s - excitation Excitation by circularly polarized laser Selective detection of σ ± component s - s + η = I + I I + + I 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 2 MoSe 2 MoS 2 WS 2 PL 63 % 5 % 56 % 42 %

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

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

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

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). σ -K K σ + 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, (2014). D. MacNeil et al., PRL 114, (2015). A. Srivastava et al., Nat Phys 11, 141 (2015). G. Aivasian et al., Nat Phys 11, 148 (2015).

17 Berry curvature in monolayer MoS2 :wave vector :Bloch function T. Cao et al., Nat. Comm. 2, 887 (2012)

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

19 Spontaneous Hall effect Various Hall effect Theory electron / hole phonon spin valley magnon exciton optical response composite particles Anomalous velocity 1 E( k) 1 r ( r) Ωk ( ) k Potential gradient e.g. electric fields E Berry curvature internal magnetic field Hall effect of excitons??? Exciton with finite Berry curvature W. Yao et al., Phys. Rev. Lett. 101, (2008). S. I. Kuga et al., Phys. Rev. B 78, (2008). Candidate: Valley excitons in TMDs!! 19

20 Valley Hall Effect in TMD monolayer 1 E( k) 1 r ( r) Ωk ( ) k Potential gradient e.g. electric fields E Berry curvature effective magnetic field J. Lee et al., Nature Nano 11, 421 (2016) K. F. Mak et al. Science 344, 1489 (2014)

21 Valley Hall effect in monolayer MoS2 Electrical detection of the optically excited electrons and holes 1 E( k) 1 r ( r) Ωk ( ) k σ + σ - K. F. Mak et al. Science 344, 1489 (2014)

22 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 r ( r) Ωk ( ) k J. Lee, K. F. Mak et al., Nature Nano 11, 421 (2016)

23 Valley Hall Effect in TMD monolayer 1 E( k) 1 r ( r) Ωk ( ) k Potential gradient e.g. electric fields E Berry curvature effective magnetic field J. Lee et al., Nature Nano 11, 421 (2016) K. F. Mak et al. Science 344, 1489 (2014) Theory of valley-nernst effect S. Konabe et al. PRB 90, (2014).

24 Valley Hall Effect in TMD monolayer 1 E( k) 1 r ( r) Ωk ( ) k Potential gradient e.g. electric fields E Berry curvature effective magnetic field J. Lee et al., Nature Nano 11, 421 (2016) K. F. Mak et al. Science 344, 1489 (2014) Exciton Hall effect

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

26 PL mapping in monolayer MoS2

27 Observation of exciton Hall effect Polarization-resolved PL mapping(pumped by linearly polarized light) (under B = 0 ) 1 mm

28 Observation of exciton Hall effect Polarization-resolved PL mapping(pumped by linearly polarized light) I I I s s (under B = 0 ) -3 3

29 Trajectories of Hall effect Color mapping of I 1 Conventional Hall effect 0 h e - -1 Hall effect of excitons, visible objects. Tracing trajectories M. Onga et al., Nature Materials 16, 1193 (2017)

30 Hall angle of exciton hall effect Definition & evaluation Lxy EHE L xx Large Hall angle ( real space observation) L xy L xx Sample dependence # EHE cf. Valley Hall Effect 10 3 K. F. Mak et al., Science 344, 1489 (2014). Trion Exciton 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). 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, (2016)

31 FET and EDLT (Electric Double Layer Transistor) FET Electric Double Layer Transistor (EDLT) Insulator Semiconductor Metal Electronic phase transitions

32 TMD-EDLT FET vs EDLT (WSe 2 ) S D Carrier density (WSe 2 ) EDLT 220K I DS (A) FET I DS (A) MoS 2 WSe 2 n 2D (x10 13 /cm 2 ) 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 (Zhang et al., Nano Lett. (2012))

33 Field-induced p-i-n Junction Output curve 40 V G G = = 22 V Cool down here 30 I DS (ma) V DS (V) 3 4 V 4T (V) S V V V D V DS (V)

34 Field-induced p-i-n Junction 20 Output curve I DS (ma) K 150 K V DS (V) Zhang et al., Nano Lett. (2013) Hall effect measurement R H1 R H /cm /cm 2 R H1 ( ) 0 R H2 ( ) B (T) B (T)

35 Electroluminescence from WSe 2 Au/Ti 5 μm EL intensity (a.u.) Bias current (ma) Bias Absorption PL intensity A-exciton B-exciton RT He et al., PRL (2014) RT excitation 2.33 ev 100 K 6V 5V 4V 3V 2V EL intensity Photon energy (ev) 100 K 2.2 Y. J. Zhang et al., Science 344, 725 (2014)

36 Electroluminescence from WSe 2 Current-induced circularly polarized EL 40 K EDL gating EL intensity (a.u.) s- s Photon energy (ev) Y. J. Zhang et al. Science (2014) Simultaneous publications SiN gating: Pospischil et al. Nat. Nano. (2014) HfO 2 gating: Baugher et al. Nat. Nano. (2014) hbn gating: Ross et al. Nat. Nano. (2014)

37 Electronic structure of gated multilayer MoS n(z) Real space (SC state) Quasi-monolayer SC z E Gated multilayer is a mimic of monolayer H. T. Yuan et al., Nat Phys (2013) M. S. Bahramy T. Brumme et al.. Phys. Rev. B 91, (2015)

38 Electrical Control of Circular Polarization Field-effect doping is reversible and tunable Modulation of diode profile WSe K Circularly polarized light source showing electrical controllability Y. J. Zhang et al. Science (2014)

39 Circularly Polarized EL from MoSe 2 6 K MoSe K EL intensity (a.u.) Photon energy (ev) 1.60 M. Onga, et al. APL (2016).

40 Optical filter Helical Light Generation Angular momentum selection rule Spin LED Valley LET Structure Konishi et al., PRL. (2011) Yang et al., Adv. Mater. (2013) Helicity control needs spin (External magnetic field) Helicity can be controlled by current (External in-plane electric field)

41 Gate induced superconductivity in MoS V EDLT =0V 10 5 R s ( ) V EDLT =6V T (K) J. T. Ye et al. Science 338, 1193 (2012)

42 MBE (layer-by-layer growth) Newly emerging 2D superconductors CVD mechanically-exfoliated (2D crystals) Ionic gating (EDLT) Pb, In single layer (1L) Nature Phys. 6, 104 (2010). PRL 107, (2011). Tl-Pb single layer (1L) PRL 115, (2015). FeSe-1L CPL 29, (2012). Heavy Fermion superlattice Nature Phys. 7, 849 (2011). Mo 2 C-1~2L Nature Mat. 14, 1135 (2015). BSCCO-1L Nature Comm. 5, 5708 (2014). NbSe 2-1L Nano Letter 15, 4914 (2015). Nature Nanotech. 10, 765 (2015). intercalated graphene PNAS 112, (2015). ACS Nano 10, 2761 (2016). STO & KTO Nature Mat 7, 855 (2008). Nature Nano. 6, 408 (2011). Cuprate (LSCO) Nature 472, 458 (2011). ZrNCl-quasi-1L Nature Mat. 9, 1314 (2010). Science 350, 409 (2015). TMDCs-quasi-1L Science 338, 1193 (2012). Sci. Rep. 5, (2015). Nature Nano. 11, 339 (2016). Nature Phys. 12, 144 (2016).

43 2D superconductors Y. Saito et al. Nature Reviews Materials 2, (2016)

44 EDLT: New platform of 2D superconductivity (materials) SrTiO 3, KTaO 3, LSCO, YBCO ZrNCl, MoS 2, MoSe 2, TiSe 2, FeSe, (weak pinning) (broken inversion symmetry) Quantum Phase Transition Saito, Science (2015), Nat Comm (2018) Enhanced Hc2 by SOI Saito, Nat Phys (2016) Nonreciprocal Supercurrent Wakatsuki/Saito, Sci Adv (2017) Qin, Nat Comm (2017)

45 Noncentrosymmetric superconductors Rashba-type spin polarization Parity mixture CePt3Si CeRhSi3, CeIrSi3, Uir, Li2Pt3B, Li2Pd3B, Benchmark; Enhanced Pauli limit P H c 2 To observe Pauli limit, Maki parameter Two ways Heavy electron mass Reduced dimensions 2 H 2 1 H orb c P c2

46 Monolayer MoS 2 ; a new class of noncentrosymmetric SC Trigonal structure with simple band structure with out-of-plane spin polarization n(z) Quasi-monolayer SC DFT calculation~ 1 layer Brumme et al., PRB 91, (2015). z 2H-type structure E

47 R-T Curves for H and H // (MoS 2 ) c q H H H

48 Thickness of superconductivity in MoS 2 -EDLT 20 Pauli limit 2D Tinkam model H c2 ( T ) GL (0) (1 T / T c ) B c2 (T) H H H c2// ( T ) (0) d GL d SC 1.4 nm sc (1 T / T c ( 0 = h/2e) ) 1/ 2 5 GL (0) 8.1 nm T (K) Cf. EDA monolayer T. Brumme et al., PRB91, (2015).

49 High field measurement at ISSP, Univ Tokyo on gated MoS 2 H Experiment 2D GL (orbital limit) Enhanced Pauli limit conventional Pauli limit Y. Saito et al., Nature Physics 12, 144 (2016).

50 Zero-field Zeeman splitting in conduction band in gated MoS 2 M. S. Bahramy Zeeman splitting (E F ) = 13 mev Intervalley pairing s + f symmetry FFLO

51 H Comparison with Theory for MoS 2 Experiment Theory (Pauli limit) 2D GL (orbital limit) Rashba Zeeman Enhanced Pauli limit conventional Pauli limit M. S. Bahramy Y. Nakamura and Y. Yanase H c2 : semiquantitatively explained by Zeeman type spin-valley locking Further theory Ilic et al.. PRL 119, (2017) 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)

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