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Condensed Matter Physics At Low Dimensions

Condensed Matter Physics At Low Dimensions. Philip Kim Department of Physics Columbia University. Condensed Matter Physics. ~10 23 electrons ~10 23 ions. Atomic orbital sp 2. 0D. 1D. 2D. 3D. Carbon Nanotubes. Fullerenes (C 60 ). p. s. SP 2 Carbon: 0-Dimension to 3-Dimension.

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Condensed Matter Physics At Low Dimensions

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  1. Condensed Matter Physics At Low Dimensions Philip Kim Department of Physics Columbia University

  2. Condensed Matter Physics ~1023 electrons ~1023 ions

  3. Atomic orbital sp2 0D 1D 2D 3D Carbon Nanotubes Fullerenes (C60) p s SP2 Carbon: 0-Dimension to 3-Dimension Benzene molecule Graphene Graphite

  4. E(k2D) E empty ky' kx' filled ky K’ K x ky kx kx 2D Brillouin Zone Electronic Band Structure of Graphene Band structure of graphene (Wallace 1947) A B Zero effective mass particles moving with a constant speed vF = c/300

  5. Spinor Representation q ‘B’ sublattice : pz orbitals Superposition: Spin Single Layer Graphene: Pseudo Spinor ‘A’ sublattice: pz orbitals Graphene Lattice Structures [ ] Cs X Two inequivalent lattice sites! Pseudo spin

  6. E E momentum pseudo spin ky ky kx kx 1 Effective Dirac Equations . = eik r eiqk qk = tan-1(ky / kx) G. SemenoffPRL (1984) Dirac Fermions in Graphene : “Helicity” E K K’ ky kx

  7. B s s Hall (1879) Hall Effect Rxx = Vxx / I Rxy = Vxy / I = B/en Rxy Quantum Hall Effect: Klitzing (1980) I + - Rxx Vxy + - Vxx + - Quantized Cyclotron Orbit + -

  8. spin (2) X pseudo-spin (2) Quantization: _ e __ 1 2 -1 4 (n + ) Rxy= pseudo-spin rotation h 2 E Quantum Hall Effect in Graphene (2005) kx' ky'

  9. Klein Tunneling (1928) Step Potential problem V>m: transmission via negative energy states E filed V V V 0 0 0 x x x Klein result: barrier sharpness ~Compton wavelength

  10. 1 mm Klein Tunneling and Pseudo spin electrode Chiral tunneling in graphenepn junctions VBG > 0 VTG < 0 VBG < 0 VTG > 0 graphene p n n p p n 20 nm Katsnelson et al. (2006) -1 0 +1 Gosc (e2/h) Magnetic field modulation of FP |n2| (1012 cm-2) Young et al. (2009)

  11. Spin ½ and Electron Interaction “Triplet” Exchange Interaction: “Singlet” Pseudo Spin “Quantum Hall bilayer” “Valley spin” …

  12. q Spin SU(4) Quantum Hall Ferromagnet in Graphene < SU(4) E Anti FerroMagnetic Charge Density Wave FerroMagnetic ky kx Kekule Distortion K’ K’ Degree of freedom: Spin (1/2), Valleys Under magnetic fields: pseudospin= valley spin Magnetic Wave Function Yang, Das Sarma and MacDonal, PRB (2006); Possible SU(4) Quantum Hall Ferromagnetism at the Neutrality y X K y K y K’ y Valley spin K’

  13. Spin & pseudo spins: many body physics in graphene Dean et al. Nature Physics (2011) 5 mm Mobility > 300,000 cm2/Vsec • SU(4) hierarchical Fractional Quantum Hall Effect • Spin and Pseudospin Ferromagnetic Quantum Hall Effect • Spin Skyrmion and Valley Skyrmions

  14. Phase Transitions in Lowest Landau Levels Phase Transitions Among Fractional Quantum Hall States Bilayer Graphene Encapsulated with top & bottom gate sxx (S) mobility > 106 cm/Vsec E-field tunable FQHE Bilayer graphene: Fractional Quantum Hall effect Rxx (kW) 8/3 2/3 5/3 1 2 3 4 5 6 20 mK 2/3 4/3 5/3 7/3 8/3 10/3 11/3 Maher*, Wang* et al. submitted

  15. Assembly of Various 2D Systems Charge Transfer Bechgaard Salt graphene Metal-Chalcogenide Bi2Sr2CaCu2O8-x C (TMTSF)2PF6 hexa-BN X Lead Halide Layered Organic M B N X M = Ta, Nb, Mo, W, Eu… X = S, Se, Te, … Semiconducting materials: WSe2, NbS2, MoS2, … Complex-metallic compounds : TaSe2, TaS2, … Magnetic materials: EuS2, EuSe2 ,… Superconducting: NbSe2, Bi2Sr2CaCu2O8-x, ZrNCl,… A C A B A

  16. Andreev Reflections – between NbSe2 & Graphene Efetov et al. (2014) Superconductivity and QHE NbSe2 Tc= 7 K Hc2 = 4.5 T graphene 5 mm Andreev Reflection btw graphene/NbSe2 Andreev Reflection Tomasch Oscillations 1.5 K 2.5 K 3.5 K 4.5 K 5.5 K 6.5 K 6.8 K 7.0 K 7.2 K 7.5 K Andreev Reflection into QH edge states are more efficient!

  17. Atomically Thin vdW p-n junction C. Lee et al, submitted Vertical & Lateral Channels - Al contact to MoS2 for electron injection - Pd contact to WSe2 for hole injection Gate Tunable Diode Characteristic Lateral and vertical electron band alignment Lateral Transport in Channels Forward Interlayer recombination by inelastic tunneling process

  18. Graphene Materials and Applications Printable Inks Transparent Electrodes Flexible/Transparent Electrodes/Touch Panels Conductive Ink, EMI shields Large-Scale CVD Graphene + Graphene Nanoplatelet Composites Gas Barriers Semi-conductors Ultrafast Transistors, RFIC, Photo/Bio/Gas Sensors Gas barriers fo Displays, Solar Cells Energy Electrodes Heat Dissipation Composites LEDLights, BLU ECU, PC … Super Cap./Solar Cells Secondary Batteries Fuel Cells Cars, Aerospace Appliations Images: Royal Swedish Academy Courtesy: B. H. Hong

  19. Relativistic QM: High Energy Physics . Dirac Equation: Kim Lab @ Columbia in City of New York CERN Electro-Positron Collider Conclusions Quasi Relativistic QM: Low Energy Physics MajoranaEquation: ??

  20. Acknowledgement Patrick Maher Carlos Forsythe Giselle Elbaz (jointly with Brus group) Austin Cheng Frank Zhao Xiaomeng Liu Amelia Barreiro Chul-ho Lee (jointly with Nuckolls group) Jean-Damien Pillet Jayakanth Ravichandran Adam Wei Tsen (jointly with Pasupathy group) Dmitri Efetov Fereshte Ghahari Collaborators Horst Stormer, Aron Pinczuk, Tony Heinz, Abhay Pasupathy, Latha Venkataraman Louis Brus, George Flynn, Colin Nuckolls, Jim Hone, Ken Shepard, Louis Campos, Rick Osgood T. Taniguchi, K, Watanabe Andre Geim, Kostya Novoselov, Sanka Das Sarma Current Members Yue ZhaoMitsuhide TakekoshiAndrea YoungDmitri EfetovFereshte GhahariPatrick Maher Young-Jun Yu (jointly with GRL, POSTECH)Vikram Deshpande (jointly with Hone group)Paul Cadden-Zimansky (Columbia Frontier of Science Fellow)Chenguang Lu (jointly with Hone and Herman Collaborating Students/postodcs Cory Dean, Inanc Meric, Lei Wang, Sebastian Sorgenfrei, Kevin Knox, Nayung Jung, Seok Ju Kang, Jun Yan, Yanwen Tan, Kevin Knox Past Members Melinda Han (Ph.D. 2010, Frontier of Science Fellow, Columbia University) Meninder S. Purewal (Ph.D. 2008) Josh Small (Ph.D. 2006) Yuanbo Zhang (Ph.D. 2006, Professor, Fundan University) Yuri Zuev (Ph.D. 2011, IBM Fishkill) Kirill Bolotin (Assistant Professor, Department of Physics, Vanderbilt University) Byung Hee Hong (Associate Professor, Department of Chemistry, Seoul National University) Pablo Jarillo-Herrero (Assistant Professor, Department of Physics, MIT) Keunsoo Kim (Assistant Professor, Department of Physics, Sejong University) Namdong Kim (Research Scientist, POSTECH) Barbaros Oezyilmaz (Assistant Professor, Department of Physics, National University of Singapore) Collaborations: Brus, Dean, Heinz, Hone, Nuckolls, Shepard Funding: Kim group and friends (2011)

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