Topology and Correlations in Monolayer Crystals. Sanfeng Wu Department of Physics, MIT UCAS

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1 Topology and Correlations in Monolayer Crystals Sanfeng Wu Department of Physics, MIT UCAS

2 Topology and Correlations Quantum Hall Effects Experimental milestones in 1980s: Klaus von Klitzing; Daniel C. Tsui; Horst Ludwig Störmer; Robert B. Quantum Laughlin Hall Phases Non-Abelian Anyons High-Tc Superconductivity Georg Bednorz; K. Alex Müller Superconductivity Data by Eisenstein and Stormer Cuprates Topological Quantum States Correlated Quantum States

3 magnetic field Topology and Correlations Quantum Hall Phases 5/2 FQH state Topological Insulator Quantum Anomalous Hall State Lu et al, Science 2015 Superconductivity 0 carrier density

4 magnetic field Topology and Correlations Quantum Hall Phases New Territory e.g. Topological superconductivity & non-abelian anyons Superconductivity carrier density

5 Monolayer Crystals and Heterostructures The simplest materials hosting 2D electrons: (Isolated) Crystalline Atomic Monolayers Mechanical Exfoliation Optical image MBE/CVD/PVD Growth Heterostructures monolayer stamp Monolayer tape Geim et al MoS 2 Large area, scalable Van der Waals Heterostructure 1mm Wu*, Huang*, et al, ASC Nano (2013) Image: Novoselov et al, Science (2016)

6 My Research Interests & Today s Topic A Large Family of Monolayer Crystals (many to be explored) CrI 3 (2017) Magnet WTe 2 (2017) Topological Insulator & Superconductor Topological States Topological States of Matter of Matter e.g., QSHE, QAHE Non-abelian e.g., QSHE, anyon QAHE Non-abelian anyon New New Types Types of of Superconductor Superconductor e.g., Unconventional e.g., Unconventional High-Tc High-Tc Quantum Device Quantum Applications Device Applications Monolayer Quantum WTe information 2 e.g., Topological electronics e.g., Topological electronics Quantum Optoelectronics information Optoelectronics Graphene (2004) Semimetal Quantum spin Hall effect in monolayer WTe 2 Superconductivity in monolayer WTe 2

7 Experimental Quantum Spin Hall Effect 2D time-reversal invariant topological insulators Semiconductor Heterostructures Molenkamp & Zhang et al (HgTe, 2007) Du et al (InAs/GaSb, ~ 2015) Low Temperature Phenomena: Near Liquid Helium Temperature (< 10 K)

8 Monolayer QSH Systems Spin-orbit coupled Graphene, 2005 Kane&Mele Bismuth Bilayer, 2006 Yazdani, Murakami, Palacios etc Stanene, 2013 S.C. Zhang et al Silicene and Germanium, 2011 Y. Yao et al Transition Metal Dichalcogenides Qian, Liu, Fu and Li, Science (2014) Others: GaBiCl 2 BiX/SbX ZrBr ZrTe 5 Bi 4 F 4 Bi 4 Br 4 TaCX (X=Cl, Br, I) MC (M = Zr, Hf ).

9 Monolayer Transition Metal Dichalcogenides M = Mo, W; X = S, Se, Te. 1T TMD Monolayer

10 Signatures of QSHE in a 2D time reversal invariant TI Drain Source Helical edge mode of a insulator Topological protection allowed by TR symmetry Expected QSH Transport Signatures: Bulk insulating + edge conducting Quantized conductance, ~ e 2 /h per edge Conductance saturates in the short-edge limit Quantization destroyed under broken TR symmetry (Zeeman gap opening at the Dirac point)

11 Quantum Transport in Atomically Thin WTe 2 Graphite BN WTe 2 F. Zheng, et al. Adv. Mat WTe2 BN Electrodes Fei, Palomaki, Wu,, Xu, Cobden et al, Nature Physics, 2017

12 Edge Conduction in Monolayer WTe 2 Distinguish Edge Conduction from the Bulk Contribution Gate (V) Expected QSH Transport Signatures: Bulk insulating + edge conducting Quantized conductance, ~ e 2 /h per edge Conductance saturates in the short-edge limit Quantization destroyed under broken TR symmetry (Zeeman gap opening at the Dirac point) Tang et al, Nature Physics (2017)

13 Is It Really a QSH Insulator? Difficulties Good Contact? High Quality Devices? How to do length dependence properly? Graphite Gate, V tg BN BN WTe 2 BN BN Electrodes Channel Length L c Doped Doped

14 ΔR (h/e 2 ) Helical Edge Mode: Conductance Quantization 1 L c 0.75 undoped 0.5 h/2e nm,Device 2 100nm, Device1 70nm, Device 2 doped Local Gate (V)

15 Edge Resistance (h/e 2 ) Helical Edge Mode: Length Dependence h/2e Length(nm)

16 G edge (e 2 /h ) Helical Edge Mode: Breaking Time-Reversal Symmetry Local Gate (V) T G (e 2 /h) T 2 8 B (T) 34T (K) L n(g /G 0 ) G = G 0 exp (- g u B B/2K B T), g ~ 4.8 Zeeman Gap Opening at the Kramers point (Dirac Point) µ B B / k B T 0 8 T Increasing B

17 G (e 2 /h) G edge (e 2 /h ) Helical Edge Mode: Breaking Time-Reversal Symmetry Local Gate (V) T T 10 0 c a. - 6 V 6.85V V V c = V 10-2 b B (T)

18 Observation of the QSHE in Monolayer WTe 2 BN Graphite Gate BN Electrodes Expected QSH Transport Signatures: Bulk insulating + edge conducting Quantized conductance, ~ e 2 /h per edge Conductance saturates in the short-edge limit Quantization destroyed under broken TR symmetry (Zeeman gap opening at the Dirac Point) Spin-polarized edge transport Non-local quantum transport Exotic phenomena allowed by QSHE

19 Channel Conductance (e 2 /h) The High Temperature QSHE V c V - 7 V T (K) 12 years after the prediction of QSHE in graphene, we report strong evidences of QSHE in a monolayer crystal. 10 years after the first QSH experiment, we observed the expected Dirac-point behavior. We achieved the QSHE at high temperatures. Wu*,#, Fatemi*,#, Gibson, Watanabe, Taniguchi, Cava, and Jarillo-Hererro # to appear in Science (2017) Recent ARPES/STM Measurements: 45 mev gap in the bulk Tang et al, Nature Physics (2017); Jia et al, PRB (2017)

20 Four Probe Conductance (us) Resistance (KΩ) Superconductivity in Electrostatically Doped Monolayer WTe K 100 Metallic QSH insulator 20 IV Characteristic Gate Voltage (V) T c ~ 1K for highest gate voltage Bulk WTe 2 : Tc ~ 6.5 K under high pressure Kang et al, Nat. Commun. 6, 8804 (2015) Pan et al, Nat. Commun. 6, 8805 (2015)

21 Gate Tunable Superconductivity -1.5V Undoped V 5V Electron doped 50% Estimated Critical Density: ~ 5x10 12 cm -2 Another device ~ 3x10 12 cm -2 SC Fatemi*, Wu*,#, Cao, Bretheau, Gibson, Watanabe, Taniguchi, Cava, and Jarillo-Hererro # Submitted (2017)

22 Monolayer WTe 2 : A Low Density Superconductor 2D Superconductors and their carrier densities. MoS 2 (ionic gating) Monolayer WTe 2 LAO/STO Cuprates TiSe 2 (ionic gating) n 2D cm -2 Monolayer WTe 2

23 The Time Before History History and the Future of History 上古结绳而治, 后世圣人易之以书契 B.C.E 中国历史 The Knotting Age 结绳记事 伏羲 (3000 ~ 5000 B.C.E) The Scratching Age 刻划记事 2017 C.E A New Knotting Age? 量子结绳记事?

24 Acknowledgements Work at MIT Pappalardo Fellowships in Physics Pablo Jarillo-Herrero Valla Fatemi (MIT) Quinn Gibson & Robert J. Cava (Princeton) Kenji Watanabe & Takashi Taniguchi (NIMS) Liang Fu (MIT) Work at UW Xiaodong Xu David Cobden (UW) Zaiyao Fei (UW) Wang Yao (HKU) Di Xiao (CMU) Jiaqiang Yan & David Mandrus (ORNL)