Coulomb Drag in Graphene

Transcription

1 Graphene 2017 Coulomb Drag in Graphene -Toward Exciton Condensation Philip Kim Department of Physics, Harvard University

2 Coulomb Drag Drag Resistance: R D = V 2 / I 1 Onsager Reciprocity V 2 (B)/ I 1 = V 1 (-B)/ I 2 Price et al., Science (2012) Coulomb drag between graphene/nanotube Drag in graphene Drag in nanotube Pillet et al., arxiv:

3 Excitons Excitons in Semiconductors E e k ex k h Direct and indirect excitons in semiconducting quantum wells Spontaneous coherence Semiconductor heterostructure + - A. High, Nature 2012

4 Excitons in 2D Materials TMDC (MX 2 ) Strong confinement Lack of strong screening effect Spin polarized band Spin-valley locking

5 Interlayer Excitons in TMDCs MoSe 2 /WSe 2 heterostructures Intralayer excitons Gate dependent photo luminescent Interlayer excitons MoSe 2 WSe 2 L. Jauregui et. al, unpublished (Collaboration with H. Park and M. Lukin groups)

6 Exciton condensation between Landau levels J. P. Eisenstein, Annu. Rev. Condens. Matter Phys. 5, 159 (2014). Two partially filled Landau levels B

7 Exciton condensation between Landau levels J. P. Eisenstein, Annu. Rev. Condens. Matter Phys. 5, 159 (2014). Two partially filled Landau levels B GaAs Double Quantum Well Total Landau level quantum Hall effect Quantum Hall effect for two partially filled complementary LLs Quantized drag Hall M. Kellogg, et. al, PRL (2002)

8 Exciton Condensation: Currents Exciton condensation (exciton insulator) Counter Flow Symmetric Flow Exciton condensation between LL (topological exciton insulator)

9 Exciton Current and Quantized Drag

10 Outlines Frictional magneto-coulomb drag in graphene hexa boron nitride heterostructure Frictional magneto drag effect in semiclassical regime arxiv: Quantized drag in excitonic regime arxiv:

11 Coulomb Drag Experiment in Graphene e-e drag: negative e-h drag: positive h-h drag: negative

12 Coulomb Drag in Double Layer Graphene T = 300 K Drag resistance sign reversal at the double neutrality point Manchester group, Nature Phys. 8, 896 (2013) Xiaomeng Liu et al, arxiv:

13 Temperature Dependent Coulomb Drag 300 K 250 K Drag Resistance at Double Neutrality 200 K 175 K Nature Phys. 8, 896 (2013) Xiaomeng Liu et al, arxiv: Manchester group

14 Interaction dominates at DNP (Schutt et al, PRL 110, (2012)) Possible Scenarios Energy vs. momentum drag (Song and Levitov, PRL 109, (2012)) -correlated disorder -anti-correlated disorders PRL 109, (2012) Strain induced (Gibertini et al., Phys. Rev. B 85, (2012))

15 Sign of Drag Near the Neutrality

16 Magneto Drag in Graphene R drag xx (W) R drag xy (W) B = 1 T T = 150 K T = 70 K Xiaomeng Liu et al, arxiv:

17 Magneto Drag in Graphene at High Magnetic Field B = 13 T R drag xx (W) R drag xy (h/e 2 ) T = 70 K Finite drag signal only when the LLs are partially filled. No drag if either layer becomes incompressible Xiaomeng Liu et al, arxiv:

18 Correlation Between Drag and Transport Measured Magneto and Hall Resistance r bottom r top xx top xx (W) r bottom xy (W) (W) Measured magneto and Hall drag Calculated magneto and Hall drag GaAs 2DEG r xxd (W) r xyd (W) r xxd (W) r xyd (W) Xiaomeng Liu et al, arxiv:

19 Quantitative Comparison OSS PRL (2001) Components of drag tensor follows a similar scaling prefactor. Xiaomeng Liu et al, arxiv:

20 Double Bilayer Graphene Drag Device Mobility ~ 10 6 cm 2 /Vsec hbn thickness d =3 nm top and bottom gate contact gate interlayer bias Xiaomeng Liu et al, arxiv:

21 Resistance (kw) Bilayer Graphene/hBN/Bilayer Graphene: Quantized Hall Drag Mobility ~ 10 6 cm 2 /Vsec hbn thickness d =3 nm Hall Resistance, Magneto Drag, and Hall Drag n bot =n top =1/2; n tot =1 top and bottom gate contact gate interlayer bias n =1 n =4/3 n =2 Xiaomeng Liu et al, arxiv:

22 Exciton BEC Energy Scale and Counter Flow Superfluidic Counter flow

23 Quantized Hall Drag for n tot = 1 and 3 Partial coherent exciton current: Partially filled N top =1 Partially filled N bot =3 E top E bot Coherent exciton current: Partially filled N top =1 Partially filled N bot =1 E top E bot

24 Magneto Exciton Condensation in Different LLs Observed Exciton condensations (0.5, 0.5) (0.5, 2.5); (2.5, 0.5) (-0.5, -0.5) Possible n -> n +2 symmetry in bilayer graphene double layer Other possible Exciton Condensation Li et. al., arxiv:

25 Effect of Interlayer Bias Voltage Interlayer Bias voltage dependence (0.5, 0.5) Interlayer bias voltage can be controlled the displacement fields on BLGs Interlayer Bias voltage dependence Exciton BEC

26 Quantum Hall Ferromagnetic Phase Transition in Bilayer Graphene Bilayer Landau level spectrum: SU(4) and SU(8) Each Landau level is degenerate for spin and valley except zero energy LL where there is an additional accidental degeneracy n =0,1. 4: (n =3; K,K ; +s) _ 4: (n =2; K,K ; +s) _ 8: (n =0,1; K,K ; +s) _ 4: (n =2; K,K ; +s) _ 4: (n =3; K,K ; +s) _ Broken Symmetry Gap in Bilayer due to Interaction: Tuned by displacement field (pseudo magnetic field) B. M. Hunt etc. (2016).

27 Exciton BEC Phase Transition: Internal Degree of Freedom of Exciton Appearance of BEC closely related to wave function of BLG Strength of BEC controlled by layer/valley polarization (kw) Internal degree of freedom of excitons can be controlled and incur phase transitions in the BEC.

28 Summary and Outlook Semiclassical Coulomb drag in the presence of thermal fluctuations Quantum drag Hall effect and robust magneto exciton condensation Exciton condensation between different Landau levels Phase transition between different exciton condensations Moving forward: Double monolayer, resonance tunneling, phase transition in BEC, exciton insulator (B=0), fractional excitons,.

29 Acknowledgements Harvard University Xiaomeng Liu Bert Halperin NIMS, Japan Takashi Taniguchi Kenji Watanabe CNS (Fabrication facility) Columbia University NHMFL Cory Dean, Patrick Maher, Lei Wang, K.C. Fong, Jim Hone Funding: