Condensed Matter Physics At Low Dimensions Philip Kim

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

Condensed Matter Physics ~1023 electrons ~1023 ions

SP 2 Carbon: 0 -Dimension to 3 -Dimension p Benzene molecule 0 D Fullerenes (C 60) s Atomic orbital sp 2 1 D Carbon Nanotubes 2 D Graphene 3 D Graphite

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

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

Dirac Fermions in Graphene : “Helicity” E E momentum pseudo spin E K’ kx ky ky kx Effective Dirac Equations G. Semenoff PRL (1984) K kx ky = eik. r 1 e iq qk = tan-1(ky / kx) k

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

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

Klein Tunneling (1928) ile d Step Potential problem Ef V>m: transmission via negative energy states V 0 x Klein result: barrier sharpness ~Compton wavelength

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

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

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

Spin & pseudo spins: many body physics in graphene Dean et al. Nature Physics (2011) 5 mm Mobility > 300, 000 cm 2/Vsec • SU(4) hierarchical Fractional Quantum Hall Effect • Spin and Pseudospin Ferromagnetic Quantum Hall Effect • Spin Skyrmion and Valley Skyrmions

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

Assembly of Various 2 D Systems graphene Charge Transfer Bechgaard Salt Metal-Chalcogenide Bi 2 Sr 2 Ca. Cu 2 O 8 -x C (TMTSF)2 PF 6 hexa-BN X Lead Halide Layered Organic M B X N M = Ta, Nb, Mo, W, Eu … X = S, Se, Te, … Semiconducting materials: WSe 2, Nb. S 2, Mo. S 2, … Complex-metallic compounds : Ta. Se 2, Ta. S 2, … Magnetic materials: Eu. S 2, Eu. Se 2 , … Superconducting: Nb. Se 2, Bi 2 Sr 2 Ca. Cu 2 O 8 -x, Zr. NCl, … A C A B A

Andreev Reflections – between Nb. Se 2 & Graphene Efetov et al. (2014) Superconductivity and QHE graphene Nb. Se 2 Tc = 7 K Hc 2 = 4. 5 T 5 mm Andreev Reflection btw graphene/Nb. Se 2 Andreev Reflection Tomasch Oscillations 1. 5 K 2. 5 K 3. 5 K 4. 5 K 5. 5 K 6. 8 K 7. 0 K 7. 2 K 7. 5 K Andreev Reflection into QH edge states are more efficient!

Atomically Thin vd. W p-n junction C. Lee et al, submitted Vertical & Lateral Channels - Al contact to Mo. S 2 for electron injection - Pd contact to WSe 2 for hole injection Gate Tunable Diode Characteristic Lateral Transport in Channels Lateral and vertical electron band alignment Forward Interlayer recombination by inelastic tunneling process

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

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

Acknowledgement Amelia Barreiro Chul-ho Lee (jointly with Nuckolls group) Jean-Damien Pillet Students/postodcs Current Members Jayakanth Ravichandran. Collaborating Cory Dean, Inanc Meric, Lei Wang, Yue Zhao Adam Wei Tsen (jointly with Pasupathy Sebastian Sorgenfrei, group) Kevin Knox, Nayung Mitsuhide Takekoshi Jung, Seok Ju Kang, Jun Yan, Yanwen Tan, Andrea Young Dmitri Efetov Kevin Knox Dmitri Efetov Fereshte Ghahari Patrick 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 Patrick Maher Carlos Forsythe Giselle Elbaz (jointly with Brus group) Collaborators Austin Cheng Horst Stormer, Aron Pinczuk, Tony Heinz, Abhay Pasupathy, Latha Frank Zhao. Venkataraman Louis Brus, George Xiaomeng Liu. Flynn, Colin Nuckolls, Jim Hone, Ken Shepard, Louis Campos, Rick Osgood T. Taniguchi, K, Watanabe Andre Geim, Kostya Novoselov, Sanka Das Sarma 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) Kim 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: group and friends (2011)