Valley Hall effect in electrically spatial inversion symmetry broken bilayer graphene

NPSMP2015 Symposium 2015/6/11 Valley Hall effect in electrically spatial inversion symmetry broken bilayer graphene Yuya Shimazaki 1, Michihisa Yamamoto 1, 2, Ivan V. Borzenets 1, Kenji Watanabe 3, Takashi Taniguchi 3, and Seigo Tarucha 1, 4 1 Department of Applied Physics, University of Tokyo 2 PRESTO, JST 3 Advanced Material Laboratory, National Institute for Materials Science 4 Center for Emergent Matter Science, RIKEN

Honeycomb lattice systems 2 C Graphene N B h-bn Transitional Metal Dichalcogenides (TMDC) Metal Insulator Semiconductor: MoS 2, WSe 2, H. Zeng et al., Nature Nanotechnol. 7, 490 (2012)

Valley degree of freedom 3 Graphene TMDC Lattice Band structure -K K -K K K -K D. Xiao et al., Phys. Rev. Lett. 108, 196802 (2012) Valley degree of freedom : K or -K Valleytronics

The rise of Valleytronics 4 Light Magnetic field/spin Valley Valley Circularly polarized light T. Cao et al., Nature Commun. 3, 887 (2012) K. F. Mak et al., Nature Nanotechnol. 7, 490 (2012) H. Zeng et al., Nature Nanotechnol. 7, 494 (2012) Y. J. Zhang et al., Science 344, 725 (2014) Valley Zeeman effect Y. Li et al., Phys. Rev. Lett.113, 266804 (2014) D. MacNeill et al., Phys. Rev. Lett. 114, 037401(2015) A. Srivastava et al., Nature Phys. 11, 141(2015) G. Aivazian et al., Nature Phys. 11, 148(2015) Electric field Valley-spin coupling R. Suzuki M. Sakano et al., Nature Nanotechnol. 9, 611 (2014) TMDC (MoS 2 ) Valley Hall effect K. F. Mak et al., Science 344, 1489 (2014) Pure valley current Graphene R. V. Gorbachev et al., Science 346, 448 (2014) M. Sui et al, arxiv:1501.04685 (2015) Y. Shimazaki et al, arxiv:1501.04776 (2015) D. Xiao et al., Rev. Mod. Phys. 82, 1959 (2010) X. Xu et al., Nature Phys. 10, 343 (2014)

Inversion symmetry broken honeycomb lattice 5 Inversion symmetry broken honeycomb lattice Gap opening Berry curvature D. Xiao et al., Rev. Mod. Phys. 82, 1959 (2010)

Valley Hall effect 6 Berry curvature: Magnetic field in momentum space Acceleration Lorentz force Magnetic field k = e ħ r B Valley Hall effect Berry curvature Acceleration Velocity Velocity Anomalous velocity r = k Ω Acceleration Berry curvature Anomalous velocity D. Xiao et al, Phys. Rev. Lett. 99, 236809 (2007)

How to break inversion symmetry? 7 MoS 2 Monolayer graphene Aligned to h-bn Initially symmetry broken K. F. Mak et al., Science 344, 1489 (2014) R. V. Gorbachev et al., Science 346, 448 (2014) Structurally inversion symmetry broken system Valley Hall effect has been reported

How to break inversion symmetry? 7 MoS 2 Monolayer graphene Bilayer graphene Aligned to h-bn Top view Initially symmetry broken K. F. Mak et al., Science 344, 1489 (2014) R. V. Gorbachev et al., Science 346, 448 (2014) Structurally inversion symmetry broken system Valley Hall effect has been reported

How to break inversion symmetry? 7 MoS 2 Monolayer graphene Bilayer graphene Aligned to h-bn Top view Initially symmetry broken K. F. Mak et al., Science 344, 1489 (2014) R. V. Gorbachev et al., Science 346, 448 (2014) Structurally inversion symmetry broken system Valley Hall effect has been reported Perpendicular electric field Electrically inversion symmetry broken system Further controllability

Dual gate structure 10 Dual gate structure Independent control of Perpendicular electric field(d ) Carrier density J. B. Oostinga et al, Nature Materials 7, 151 (2008)

Dual gate structure 11 Dual gate structure + + + + - - -- --- - + + + + Independent control of Perpendicular electric field(d ) Carrier density J. B. Oostinga et al, Nature Materials 7, 151 (2008)

Dual gate structure 12 Dual gate structure - - - - + + + + Independent control of Perpendicular electric field(d ) Carrier density J. B. Oostinga et al, Nature Materials 7, 151 (2008)

Dual gate structure 13 Dual gate structure - - - - Electrical induction of Berry curvature + + + + Independent control of Perpendicular electric field(d ) Carrier density J. B. Oostinga et al, Nature Materials 7, 151 (2008) Valley Hall effect

Valley current mediated nonlocal transport 14 Nonlocal transport measurement in spintronics field Spin current detection by ISHE S. O. Valenzuela et al., Nature 442, 176 (2006) Spin current generation by SHE T. Kimura et al., Phys. Rev. Lett. 98, 156601 (2007) AFM image before top h-bn deposition Mobility ~ 15,000cm 2 /Vs

Local and Nonlocal resistance 15 T = 70K Local resistance Carrier density p n Displacement field D = D,- + D /- 2 D 12 = ε 12 (V 12 V 789 12 )

Local and Nonlocal resistance 16 T = 70K Local resistance Carrier density p n Displacement field D = D,- + D /- 2 D 12 = ε 12 (V 12 V 789 12 )

Local and Nonlocal resistance 17 T = 70K Local resistance Carrier density p n Displacement field D = D,- + D /- 2 D 12 = ε 12 (V 12 V 789 12 )

Local and Nonlocal resistance 18 T = 70K Local resistance Carrier density p n Displacement field D = D,- + D /- 2 D 12 = ε 12 (V 12 V 789 12 )

Local and Nonlocal resistance 19 T = 70K Local resistance Carrier density p n Displacement field D = D,- + D /- 2 D 12 = ε 12 (V 12 V 789 12 )

Local and Nonlocal resistance 20 Local resistance T = 70K Nonlocal resistance Carrier density p n Displacement field D = D,- + D /- 2 D 12 = ε 12 (V 12 V 789 12 ) By increasing displacement field D, non-local resistance appeared around Charge Neutrality Point (CNP)

Trivial nonlocal transport : Ohmic contribution 21 D Classical diffusive transport C I: Current L - V From van der Pauw formula L w R CDE AB = ρ π exp π L w w R CDE AB ρ + A B

Measurement result vs Ohmic contribution 22 T = 70 K Max ~ 700Ω Calculated Ohmic contribution from R CDE AB = ρ π exp π L w Max ~ 150mΩ Observed nonlocal resistance is much larger (5,000 times) than Ohmic contribuion Quantitatively not Ohmic contribution

Scaling relation between R 8O and ρ 23 Conversion ratio α = σ TU VW σ VW σ TU ρ TT Sequential conversion picture Valley Hall effect Inverse VHE (VHE) D (IVHE) I P : (Charge) current C - V Conversion ratio α = σ TU VW σ VW σ TU ρ TT Valley Hall angle SHE and ISHE mediated nonlocal transport D. A. Abanin et al., Phys. Rev. B 79, 035304 (2009) A I Q : Valley current R 8O σvw Y TU ρ Z Valid for small valley Hall angle (α 1) + B Current to voltage ρ

Scaling relation between R 8O and ρ 24 0 ~ 80meV At charge neutrality point, changed perpendicular electric field Bandgap size changes Resistivity ρ changes Valley Hall conductivity σ VW TU is constant R 8O σvw Y TU ρ Z ρ Z

Scaling relation between R 8O and ρ 25 0 ~ 80meV 0meV Bandgap 80meV R 8O σvw Y TU ρ Z ρ Z Cubic scaling Transport mediated by pure valley current T=70K (k B T ~ 6meV)

Scaling relation between R 8O and ρ 26 0 ~ 80meV 0meV Bandgap 80meV Crossover behavior at high displacement field 1. Valley Hall angle α α 1 α 1 or α 1 2. Transport mechanism Band conduction Hopping conduction T=70K (k B T ~ 6meV) Open question

Valley Hall angle dependence of nonlocal resistance 27 A v ( x ) 0 E v ( x ) 0 Equations v K K v, jv : Continuous at the interface Diffusion eq. Conductance matrix j j 1 i 2 v 2 x i i c i v i v VH xx xy VH 1 xy xx 2e E i x i v w R 0 W NL exp 2 2 xx 1 Valley Hall angle: 2 VH / xy Inter-valley scattering length: λ L xx

Valley Hall angle dependence of nonlocal resistance 28 R W NL exp 2 2 xx 1 2 L Valley Hall angle: VH / xy xx For small valley Hall angle: = 1 For large valley Hall angle:? 1 R Reproduces VH 2 W xy NL exp 3 2 xx L R NL W 1 2 xx exp L D. A. Abanin et al., Phys. Rev. B 79, 035304 (2009) RNL 3 Cubic scaling Crossover RNL Linear scaling

Scaling relation between R 8O and ρ 29 0 ~ 80meV 0meV Bandgap 80meV Crossover behavior at high displacement field 1. Valley Hall angle α α 1 α 1 or α 1 2. Transport mechanism Band conduction Hopping conduction T=70K (k B T ~ 6meV) Open question

Temperature dependence 30 Band conduction Hopping conduction Insulating behavior due to gap opening Crossover behavior for both ρ E]^ and RE]^ 8O between high T and low T region Fitting function 1 ρ E]^ = 1 exp E O _ ρ _ k 1 T + 1 exp E O Y ρ Y k 1 T Band conduction (Thermal activation across bandgap) Hopping conduction (Nearest neighbor hopping) K. Zou et al., Phys. Rev. B 82, 081407 (2010) Fitting function 1 E]^ = 1 exp E _ 8O R _ k 1 T R 8O High T + 1 exp E 8O Y R Y k 1 T Low T

Activation energy 31 From R 8O ρ Z, E _ 8O = 3E _ O is expected de _ 8O dd = (3.13 ± 0.36) de O _ dd

Experiment by Fudan group 32 Gate-tunable Topological Valley Transport in Bilayer Graphene M. Sui et al., arxiv:1501.04685 (2015) Local resistance Nonlocal resistance

Summary 33 u u u u In electrically spatial inversion symmetry broken bilayer graphene, we observed the signature of valley Hall effect and pure valley current which is cubic scaling relation: R 8O ρ Z We observed the crossover behavior in scaling relation for higher displacement field region, which is still open question Nonlocal transport was detected even in insulating regime, indicates pure valley current can flow in insulating regime Our highly controllable system provides further possibility for the investigation of topological current in insulator and application to valleytronics Y. Shimazaki et al., arxiv:1501.04776 (2015)

Graphene valleytronics 34 u u u Appropriate system to study valley current transport u Graphene has long inter-valley scattering length Appropriate system for mesoscopic experiment u Super high mobility (>1,000,000cm 2 /Vs) graphene device has been reported Topological property is gate controllable u u Tunable Berry curvature Switchable valley Chern number I. Martin et al., Phys. Rev. Lett. 100, 036804 (2008)

Acknowledgements 35 u We acknowledge fruitful discussion with Prof. L. S. Levitov, Dr. J. C. W. Song, Prof. M. Koshino, Dr. M. Ezawa and Prof. N. Nagaosa