The 2nd GCOE Int’l Symposium 2 Tohoku University, Sendai, Japan Acknowledgements Feb. 18 -19, 2010
Collaborators :
UC Berkeley, USA MANA/NIMS, Japan Seoul Nat ’ l Univ Marvin L. Cohen Katsunori Wakabayashi Jungseok Chae Steven G. Louie Young Kuk Li Yang (WU at St Louis) Seoul Nat’l Univ Cheol-Hwan Park Changwon Park Konkuk Univ Relativistic Dirac Electrons in Solids G. Samsodnize Yae-Lee Lee Jinsik Choi Seungchul Kim (Upenn) Sang Ho Jeon Molecular Foundry, USA Jisoon Ihm Baeho Park ‐ Graphene Physics Jeffrey Neaton Joydeep Bhattacharjee (NISER Yonsei Univ Sogang Univ Bhubaneswar, India) Hyoung Joon Choi Duhee Yoon Hyerim Moon NREL, USA Seoul Nat’l Univ Hyeonsik Cheong Uni Choi Seungwu Han KRISS NEC, Japan POSTECH Chanyong Hwang Yoshiyuki Miyamoto Seon-Myeong Choi Young-Woo Son Hosik Lee Seung-Hoon Jhi KAIST Hu-Jong Lee Byoungjin Cho
Korea Institute for Advanced Study, Seoul, Korea Support : KOSEF, KRF, Samsung, BK21 (KOREA), NSF & DOE (US),
Supercomputing: Moelcular Foundry User Project (DOE, US),
KISTI, KIAS (Korea) NSF at NPACI, DOE at NERSC (US)
3 4 Why nano?
Energy DrasticallyDrastically different ? differentphysics and why nano and why carbon? information physicsprocessing and informationInformation processing ?
Bio-MedicineBio-MedicineManoharan, Stanford ? 5 6 Why carbon? Why carbon?
Ultimate Opto-electronic Human-Machine interface/ Nano-electronics bio-nano complex Druggy delivery
21C? Intel CPU
1960~
The first Carbon Nanopeapod B-to-Z transition of DNA Neuron growth / drug and 1947~ transistor gene delivery J. Lee, Y. Kuk, J. Ihm, G. Kim, Strano et al, Science (06) Y.-WSW. Son etlt al, Na ture (02) KfKeefer etlt al, NtNature Nano (08) / Hongjie Dai et al, ACS Nano (07)
This slides is inspired by T. Ohta at LBNL and Fritz-Haber-Institut.
7 8 CarbonWhat is allotropesgraphene? - Carbon allotropes
Graphene Brief (not comprehensive) history of ggpraphene research Graphene 9 Graphene - Statistics of recent APS March meetings • Strongest materials ever measured : Young’s modulus 1.0 Tpa
• Thinnest flexible membrane ever created 2009 APS Marc h meet ing at Pitts burg, USA
• Impermeable to gases (even atomic hydrogen) DCMP : Graphene Focus Sessions I-XIX • Highest thermal conductivity of ~5000 W/mK (Organiziers: A. H. Castro Neto, A. Lanzara, Y.-W. Son)
• Balli st ic transport over m icrometers at RT DCMP, DMP, GMAG, FIAP: 9 other sessions • Current density six order of magnitude higher than that of Cu Total 28 Sessions , ~650 talks (960 if including nanotube) • Room temperature Quantum Hall Effects → ~9% (14%) of total ~7000 talks • …. 92007 Denver Meeting 400 (800) talks out of 6800 talks 92008 New Orleans Meeting 580 (900) talks out of 6500 talks
11 12 Brief history of graphene Brief history of graphene - Early works - Early works
• Intercalated graphite as a route to graphene ! • EbdfhitlltdEnergy bands of graphite calculated L. M. Vicilis et al, Science 299, 1361 (2003). P. R. Wallace, PR 71, 622 (47). • Many important works (Dresselhaus and others)
• Condensed matter analogues to (2+1)D – QED suggested G. W. Semenoff, PRL 53, 2449 (84), E. Fradkin, PRB 33, 3236 (86), F. D. M. Haldane, PRL 61, 2015 (88) • Graphene nano-pencil ? (P. Kim@Columbia) • CbCarbon nanotbtubes !(! (Iijima, 91)
•Singgyle layer of ggpraphene gg()rown on Pt(111) and TiC(()111) substrates – CVD of hydrocarbons on metal (promising?)
T. A. Land et al, Surf. Sci. 264, 261 (()1992); A. Nagashima et al, Surf. Sci. 291, 93 (()1993) h h mcElectronic structure of graphene 13 mcElectronic structure of graphene 14 - Isolation of graphene ? - Isolation of graphene ?
15 16 Exfoliated Graphene Epitaxial Graphene - Breakthrough - Graphene electronics?
• Micromechanical cleavage of bulk graphite up to 100 micrometer in size via adhesive tapes ! • Epitaxial growth of graphene on SiC{0001}
Novoselov et al , Science 306, 666 (2004) W. A . de Heer Group at Georgia Tech C. Berger et al, Science 312, 1191 (2006)
윤두희, 정현식(서강대)
A. K. Geim Group @ Menchester P. Kim Group @ Columbia KSNK. S. Novose lov etlt al, NtNature 438, 197 (2005) YZhY. Zhang etlt al, NtNature 438, 201 (2005) • Precise control of number of layers of graphene
020.2 μm • Large scale ggpraphene productions 17 18 CVD Graphene CVD Graphene 18 - Graphene electronics? - Graphene electronics?
• Large scale graphene growth by using Chemical Vapor Deposition on thin nickel film and copper foil
Byung Hee Hong group at SKKU KSKimK. S. Kim et al, Nature 457, 706 (2009) • Transparent flexible display? Jing Kong group at MIT • Replacement of ITO? A. Reina et al, Nano Lett. 9, 30 (2009)
Rod Ruoff group at UT Austin X. S. Li et al, Science 324, 1312 (2009) • Prof. Byung Hee Hong (Chemistry, SungKyunKwan Univ, Korea) arXiv.org:0912.5485
19 20 Electronic structure of graphene - Nature of bonds in graphene
sp2 sp3
Basics of graphene physics π-orbital σ-bond
Hexagonal network of Carbon TEM imagg,e, Zettl group at UC Berkeley – sp2 bonding C. Girit et al. Science 323, 170 (2009) 21 22 Electronic structure of graphene Electronic structure of graphene - Real space - ‘Neutrino’ in your pencil?
A B
p ‐t x p y Dirac equa tion w ith zero mass charged ‘neutrino’ in your pencil?
• Relativistic particle : (()Pseudo) (()Pseudo) Two sublatticesSpin Up - BipartiteSpin Down system
c=vF: effective speed of ‘light’ m=0
24 Electronic structure of graphene Electronic structure of graphene - Low energy dispersions - Pseudospin and chiral states
Graphene Usual Semiconductor
Eigenfunctions : Spinor representation
py K+
px θp
Pseudo-spin up (down): A (B) sublattice 25 h mc 26 Electronic structure of graphene Electronic structure of graphene - Chiral states: charged “neutrino” in your pencil - Tunneling
HliitHelicity operator :
• Conduction band :
σ = -1/2 σ =+1/2= +1/2 x -e x px < 0 px > 0
A. K. Geim & P. Kim Scientific American, Apr. 2008
Electronic structure of graphene 27 Electronic structure of graphene 28 - Klein paradox - Klein tunneling
Graphene
particle
~ 2 mc 2
antiparticle
• Klein paradox: Unimpeded penetration of relativistic particles through T. A nd o, JPSJ (1992) very high potential barriers. Katsnelson et al, Nature Phys. 2, 620 (2006) 2 8 • Potential drop ~ 2 mc over h mc : ~10 V/Å V. V. Cheianov et al, Science 315, 1252 (2007) … → Event horizon of Black hole C. Park, Y.-W. Son et al, Nature Phys. (2008), → Supercritical massive atoms Phys. Rev. Lett. (2008), O. Klein, Z. Phys. 53, 157 (1929) Nano Lett (2008) 30 Transport properties of graphene 29 Electronic structure of graphene - Klein tunneling - Consequences of chiral massless Dirac fermions
Half-integer Quantum Hall Effect (Room T) ! (Manifestation of Berry’s phase of pseudospin)
Pabry-Ferot interference: observation of Berry’s phase
A. F. Younggy & P. Kim, Nature Phys. 5, 222 (()2009). N. Stander, B. Huard, D. Goldhaber-Gordon, Phys. Rev. Lett. 102, 026807 (2009)
81 years after its first prediction in particle physics, Zhang et al (05), Novoselov et al (05) condensed matter researchers confirm it in carbon Kim & Geim et al (07) nanostructure experiments. Haldane (88), T. Ando (02)
h mc 32 Electronic structure of graphene 31 Electronic structure of graphene - Consequence of chiral massless Dirac particles - Special relativity vs Superconductivity
Hall effect in superconductivity T. Sauer, Archive for History of Exact Science 61, 159 (07)
Bostwick et al, Nature Phys 3, 36 (07) Zhou et al, Nature Mat 6, 770 (07) Photoemission experiments : Crescent shape anisotropy (à la Youngg)’s double slit !) Oct. 1920 Leiden, Einstein, Ehrenfest, Langevin, Onnes
H. B. Heersc he, P. Jar illo-Herrero etlt al, NtNature 446, 56 (2007) Kim, Ihm, Choi & Son, arXiv.org:0912.1210 (09) 33 34 Controlling electronic properties of graphene Controlling electronic properties of graphene
Graphene Epitaxial Graphene Graphene Nanoribbon Epitaxial Graphene Graphene Superlattice Mass ggpgap generation due Mass ggpgap generation at the Anisotropic Dirac cone Nanoribbons Graphene Superlattices to quantum confinement Dirac point due to broken and collapse of helicity in and magnetic ordering sublattice symmetry graphene superlattice
Son, Cohen, Louie, Kim, Ihm, Choi, Son, Park, Son, Yang, Cohen, Louie, Nature 444, 347 (06), PRL 100, 176802 (08) Nature Phys 4, 213 (08), PRL 97, 216803 (06), Kim, Ihm. Choi, Son, Nano Lett 8, 2920 (08), arXiv.org:0912.1210 (09) PRL 101, 126804 (08), Yang, Park, Son, Cohen, Louie, PRL 103, 046808 (09) PRL 99, 186801 (07) Strained Graphene Lee, Ihm, Son, submitted (10) Tilted ani sot ropi c Di rac cone and tunable work functions
Choi, Jhi, Son, PRB Rapid Com, in press (10)
Choi, Jhi, Son, Submitted (10) P. Kim, P. Avouris, Hongjie Dai De Heer, Lanzara, Rotenberg Miranda, Pan, Zettl
35 Transport properties of graphene 36 - Superlattices: neutrino crystal ?
Controlling Dirac Electrons
‐ GhGraphene SlttiSuperlattice ‐
Scientific American, July 2006, J. B. Pendry & D. R. Smith 37 38 Graphene Superlattice Electron optics - Supercollimation in photonic crystals ! - Ballistic transport of electrons @ 2DEG
NEC APL (()99) Nature 422, 415 (2003)
MIT Nature Mat (06)
Collimated electrons (Quantum Hall edge states)
39 40 Graphene Superlattice Graphene Superlattice - Neutrino crystal (?) - Anisotropy from periodicity
Pristine graphene 1-D superlattice 2-D superlattice Pristine graphene 1-D superlattice 2-D superlattice
• Large scale (>>d C-C) periodic potential imposed on pristine 2-D graphene
• Low energy effective Hamiltonian approach
Park, Son, Louie et al, Nature Phys (08) Park, Yang, Son et al, Nature Phys (08) Transport properties of graphene 41 Transport properties of graphene 42 - Superlattices - Superlattices
Pristine graphene 1-D superlattice 2-D superlattice
Dirac equation Generalized Weyl’s equation Velocity decreasing Velocity does not change Slowing down group velocity (eventually to zero) : Klein tunneling
Park, Son et al, Phys. Rev. Lett. (08,09), Nano Lett (08)
44 Transport properties of graphene 43 Graphene Superlattice - Superlattices - Prediction of electron supercollimation
U=0 U=Uc From isotropic Dirac cone to wedge shape one-dimensional dispersion ! (Direct consequence of chiral nature of carriers in graphene) • One directional propagation of electron wave packet with negligible spatial sppg(ppgreading (0.1 mm propagation with 500 nm s pg)preading) • Analogue to quantum Hall edge state ? • Possible quantum interferometry Park, Son et al, Nature Phys (08), PRL (08) Park, Son et al, Nano Lett. (08) 45 Strained graphene 46
Graphene is the strongest material ever measured & the thinnest membrane ever created Electromechanical Properties of graphene
J. Hone,,() Science (2008) B. Hong, Nature ( 2009 ) N.-C. Yeh, Nano Lett (()2009)
• Strains can be applied intentionally or naturally
Strained graphene 47 Strained graphene - Previous lessons from carbon nanotubes - Electronic structures with strains from first-principles
L. Yang & J. Han, PRL 85, 154 (00) E. D. Minot et al, PRL 90, 156401 (03) • Strain along armchair direction (A-strain) • No bandgap opening up to 26 .5% strain Strained carbon nanotubes: Metal-to-Semiconductor or • Repulsion between K and K’ points Semiconductor-to-Metal transition depending on chiralities
Choi, Jhi & Son, Phy. Rev. B Rapid Com, in press (2010) (arXiv.org:0908.0977) Strained graphene Strained graphene - Electronic structures with strains from first-principles - Energy contours
Ideal 20% A-strain 20% Z-strain
• Mismatch between Dirac points and high symmetric points in • Strain along zigzag direction (Z-strain) Brillouine zone (strain as vector potential*) • No bandgap opening up to 26.5% strain • Merging two K points
* A. H. Castro Neto et al, RMP (09) F. Guinea et al, Nature Phys (09)
52 Strained graphene Strained graphene - Anisotropy in group velocity at Dirac point - Tilted anisotropic Dirac cones
ɛ=0
A-strain (%) Z-strain (%)
• Increase of velocity in direction perpendicular to strains : improvement of mobility? • Quick decrease of velocity in direction parallel to strains
• vA1 ≠ vA4 • v ≠ v Z1 Z4 Choi, Jhi,& Son, PRB Rapid Com, in press (2010) 53 Generalized Weyl Hamiltonian Strained graphene - Superlattice vs. Strains - Work functions
U (superlattice potential)
Park, Son et al, Nature Phys(08); PRL(08,09)
• Increasing work function as increasing uniaxial homogeneous strain (strain as scalar ɛ (magnitude of strain) potential)* • With very large strain, work function differs depending on the direction of strains • Controlled charge transfer between impurities (metal) and graphene by strain
* S. Ono & K. Sugihara, J. Phys. Soc. Jpn. 21, 861 (1966) H. Suzuura & T. Ando, Phys. Rev. B 65, 235412 (2002) Choi, Jhi, Son, PRB Rapid Com, in press (10) (arXiv.org:0908.0977) Choi, Jhi & Son, Phy. Rev. B Rapid Com, in press (2010)
Strained graphene Strained graphene - Work functions - Effective Hamiltonian
Effective Hamiltonian for ideal graphene
Effective Hamiltonian for strained graphene
• Isotropic strain : (almost) linear increase of work function • Strain is equivalent to effective ‘scalar potential’ Choi, Jhi, Son, PRB Rapid Com, in press (2010) No energy gap for any homogeneous strains arXiv.org:0908.0977 57 58 Electronic structures of graphene nanoribbons - Carbon nanotubes vs nanoribbons
Graphene nanoribbon physics:
application of ggpraphene
“The rise of graphene” Webpage of Shigeo Maruyama, A. K. Geim & K. S. Novoselov, Univ. of Tokyo NMilNature Materials 6, 183 (2007 )
59 60 Electronic structures of graphene Electronic structures of GNRs - Carbon nanotubes - Carbon nanotubes
mod(m-n3)=0n,3) = 0 mod(m-n3)=1n,3) = 1 Quantum Confinement
mod(m-n,3) = -1
N nanotubes:
N/3 ~ metal Iijima, 2N/3 ~ semiconductor Nature (91) 61 62 Electronic structures of GNRs Electronic structures of GNRs - Carbon nanotubes vs nanoribbons - Carbon nanotubes vs nanoribbons
Q: Carbon nanotubes (CNTs) Q: Carbon nanotubes (CNTs) can be metal or can be metal or semiconductor depending semiconductor depending on the radius of the system on the radius of the system CNT (boundary condition). CNT (boundary condition).
What about graphene What about graphene GNR GNR nanoribbons (GNRs) ? nanoribbons (GNRs) ?
A: All graphene nanoribbons are semiconductors*
*Son et al, PRL (06,07), Nature (06)
63 64 Electronic structures of GNRs Electronic structures of GNRs - Energy gap of armchair GNRs - Spin polarized edge states in ZGNRs
Spin-polarized first-ppprinciples calculation (LSDA )
All Na-AGNRs are -0.4 semiconductors with up-spin dn-spin three distinct families of ggpap size • Magnetic edge states due to infinite degenerate zero energy states Gap hierarchy:
∆3p+1 > ∆3p > ∆3p+2 (≠0) Spintronics application ?
*Son et al, PRL (06,07), Nature (06) Son et al, PRL (06,07), Nature (06) 65 66 Half-metallic graphene nanoribbons Half-metallic graphene nanoribbons - Electrical control of spin degree of freedom - Various magnetic orderings in solids
DttDatta-DDiDas Device (Quant um) S pi n H a ll Effec t Energy Energy Energy Rotation of injected spin due Accumulation of opposite spins at sample to gate electric field edges due to spin-orbit interaction
Electric field gate EF Fe 2-D Electron Gas Fe
• S. Datta and B. Das, Density of States Density of States Density of States Appl, Phys. Lett. 56, 665 (1990) Ferromagnetic Antiferromagnetic “Half-metal” metal Insulator
• G. E. W. Bauer, Science. 306, 1898 (2004)
67 68 Half-metallic graphene nanoribbons Electronic structures of GNRs - Band structures with transverse electric fields - Experiments
7 1-D variable range hopping Ion/Ioff ~10~ 10 at RT Experiment @ Columbia Univ Experiment @ Stanford Univ PRL 98, 206805 (2007) Science 319,,() 1229 (2008)
Eext=00V/Å0.0 V/Å Eext=005V/Å0.05 V/Å Eext=010V/Å0.10 V/Å • 100 % spin polarization around Fermi level (reversible and controllable organic half-metal) • Critical electric field ~ 1/width Son et al, Nature (06) 69 70 Electronic structures of GNRs Summary - New experiments from chemists 9 Graphene – the simplest complex material
9 Graphene physics – playgrounds for interdisciplinary researches
9 Physical properties of graphene are interesting and peculiar, and may be useful
J. M. Tour group (Rice Univ) Nature 458, 872 (2009) H. Dai group (Stanford Univ) Nature 458, 877 (2009)
71 72 Half-metallic graphene nanoribbons Half-metallic graphene nanoribbons - Origin of half-metallicity - ferroelectric materials PVDF – Poly ( vinylidene flouride)
H C F x z Generating strong net dipole moments from the Fluorine(F) to the hydrogen(H) x y AVA. V. Bune etlt al., NtNature 391, 874 (1998) Zhijun Hu et al., Nature Mat 8, 62 (2009)
Energy of quasilocalized states can be tunable by applying electric fields* ?
* Y.-W. Son et al, Phys. Rev. Lett. 95, 216602 (2005) 73 Half-metallic graphene nanoribbons - ferroelectric materials PVDF – Poly ( vinylidene flouride)
• 100 % spin polarization around Fermi level (reversible and controllable organic half-metal)
Yae-lee Lee, J. Ihm, Y.-W. Son, submitted (2010)