some things you might be interested in knowing about Graphene

All Natural Object/Materials Are 3D quasi-2D width length height 3D quasi-1D quasi-0D

Peierls; Landau; Mermin-Wagner; … NO Bottom-Up Approach 400 carbon atoms at 2000 K growth means temperature violent vibrations in 2D Fasolino (Nijmegen) growth of macroscopic 2D objects is strictly forbidden Peierls; Landau; Mermin-Wagner; … (only nm-scale flat crystals possible to grow in isolation)

No Bottom-Up for 2D Crystals largest known flat hydrocarbon: 222atoms/37rings (Klaus Müllen 2002) graphene: least stable configuration for <24,000 atoms (Don Brenner 2002) above this number (~20 nm), scrolls are most stable

ONE-ATOM-THICK OBJECTS, HUGE MACRO-MACROMOLECULES? (not only graphene)

one atomic plane from a bulk crystal Top-Down Approach? just extract one atomic plane from a bulk crystal

isolating individual atomic planes starting point in <<2004 suggested in print Nature Mater 2007 epitaxial growth MANY MANY DIFFERENT EPITAXIAL SYSTEMS including graphitic layers Grant 1970 (on Ru) Bommel 1975 (SiC) McConville 1986 (on Ni) Land 1992 (on Pt) Nagashima 1993 (on TiC) Forbeaux 1998 (SiC) de Heer 2004 (SiC) … … let us remove the substrate chemically, like SiN or C membranes monolayer is a part of the 3D crystal GOAL: NOT EPITAXIAL LAYERS but rather ISOLATED ATOMIC PLANES

Poor Man Approach 3D LAYERED MATERIAL extract individual atomic planes

split into increasingly thinner “pancakes” start with graphite need strong in-plane bonds Also: Kurtz 1990; Ebbesen 1995; Ohashi 1997 Ruoff 1999; Kim 2005; McEuen 2005 split into increasingly thinner “pancakes” SEM: down to ~30-100 layers 1 mm until we found a single layer called GRAPHENE one atomic plane deposited on Si wafer Manchester, Science 2004; PNAS 2005

extracting atomic planes en masse SPLIT INTO ATOMIC PLANES ANY LAYERED MATERIAL WHEN YOU KNOW THAT ISOLATED ATOMIC PLANES CAN EXIST

INTERCALATED GRAPHITE Splitting Graphite into Graphene 15 min centrifugation Manchester, Nanolett ’08 Coleman et al, Nature Nano ’08 relevant literature: INTERCALATED GRAPHITE TEM observations of ultra-thin graphite from Ruess 1948 to Boehm 1962 to Horiuchi 2004 graphene oxide paper Brodie 1859 Kohlschutter 1918 few hours sonication in organic solvent (chloroform, DMF, etc) TEM 100 nm RENAISSANCE starting with graphene oxide: Ruoff, Nature 2006 also, Kern’s, Kaner’s groups

CHEMICAL EXTRACTION chemically extract epitaxially grown atomic planes S. Seo (Samsung 2010) Kong ‘09 chemically remove the substrate FIRST DEMONSTRATED Kong et al, Nanolett 2009 on Ni Hong, Ahn et al, Nature 2009 on Ni Ruoff et al, Science 2009 on Cu as suggested, Nature Mat 2007 graphene-on-Si wafers uniform; no multilayer regions; some cracks;  >5,000 cm2/Vs

EXTRACTION ONTO SAME SUBSTRATE atomic planes decouple during cooling and/or intercalated Mallet et al 2007 special case: SiC as an insulator RELATIVELY WEAK INTERACTION WITH THE GROWTH SUBSTRATE de Heer 2004; Rotenberg 2006; Seyller 2008 DECOUPLED FURTHER BY PASSIVATION Starke 2010; Yakimova 2010

Many Other 2D Materials Possible 2D boron nitride in AFM 1m 0Å 8Å 23Å 2D NbSe2 in AFM 50 m also, 2,3,4… layers NOT ONLY NATURALLY LAYERED MATERIALS! THINK OF EPITAXY! 1 m 2D Bi2Sr2CaCu2Ox in SEM 2D MoS2 in optics 1 m Manchester, PNAS ’05

MATERIALS OF A NEW KIND: ONE ATOM THICK MESSAGE TO TAKE AWAY MATERIALS OF A NEW KIND: ONE ATOM THICK atomic planes of graphite and other materials were KNOWN before as constituents of 3D systems now we can ISOLATE, STUDY and USE them - and importantly - they are worth of!

what is so special about graphene?

GRAPHENE’S SUPERLATIVES thinnest imaginable material largest surface-to-weight ratio (~2,700 m2 per gram) strongest material ‘ever measured’ stiffest known material (stiffer than diamond) most stretchable crystal (up to 20% elastically) record thermal conductivity (outperforming diamond) highest current density at room T (106 times of copper) highest intrinsic mobility (100 times more than in Si) conducts electricity in the limit of no electrons lightest charge carriers (zero rest mass) longest mean free path at room T (micron range) completely impermeable (even He atoms cannot squeeze through)

EXCEPTIONAL ELECTRONIC QUALITY & TUNABILITY

AMBIPOLAR ELECTRIC FIELD EFFECT Manchester, Science 2004 SiO2 Si graphene CONTROL ELECTRONIC PROPERTIES homogenous electric doping from ~108 to ~1014 cm-2 ASTONISHING ELECTRONIC QUALITY -100 -50 100 50 gate voltage (V) resistivity (k) 2 4 6 ballistic transport on submicron scale under ambient conditions holes ~1013 cm-2 electrons ~1013 cm-2 weak e-ph scattering POSSIBLE ROOM-T MOBILITY above 200,000 cm2/V·s Manchester, PRL 2008 Fuhrer’s group, Nature Nano 2008 carrier mobility at 300K routinely: ~15,000 cm2/V·s

CURRENT STATUS graphene on atomically flat boron nitride  BN 10 um BN Si wafer graphene Hall bar  2 6 1 3 room-T mobility > 50,000 cm2/V·s also, Columbia group, arxiv 2010

CURRENT STATUS suspended graphene low-T mobilities few million cm2/V·s 2-terminal suspended devices: first reported by Andrei, Kim & Yacoby 2 m 2 K low-T mobilities few million cm2/V·s SdH oscillations start ~50G level degeneracy lifted ~ 500G Manchester, unpublished

UNIQUE ELECTRONIC STRUCTURE Wallace 1947

massless massive Dirac fermions chiral fermions monolayer graphene bilayer graphene McClure 1958 McCann & Falko 2006

Finding Electronic Structure B (T) 0.6 0.4 xx (k) Vg = -60V 4 12 8 10K Manchester, Science ’04 & Nature ‘05 1 25 100 50 xx (1/k) 12T Vg (V) 75 80K 140K 20K degeneracy f =4 two spins & two valleys Vg (V) 100 -50 50 -100 xx (k) 4 6 2 n =4B/φ0 ωcτ =const 8T 4K 1  (a.u.) 150 T (K) +10V +90V

Finding Electronic Structure mass of charge carriers strongly depends on concentration S ky kx E=pvF mc/m0 -3 -6 6 n (1012 cm-2) 3 0.02 0.04 0.06 vF = 1.0·106 m/s 5% ZERO REST MASS: effective mass E = mcvF2 BF =(ħ/2πe)S and mc =(ħ2/2π)∂S/∂E experimental dependences BF ~ n and mc ~ n1/2 necessitates S ~ E(k)2 or E ~k in agreement with theory: Wallace 1947, McClure 1958, Semenoff 1984

massive & massless Dirac fermions half-integer QHE relativistic analogue of integer QHE “anomalous” QHE n (1012 cm-2) -2 -4 4 2 5 10 1.5 -1.5 -2.5 -3.5 -0.5 2.5 3.5 0.5 12T xx (k) xy (4e2/h) xy (4e2/h) xx (k) n (1012 cm-2) -2 -4 4 2 6 1 -1 -3 3 12T 4K Manchester, Nature ’05; Columbia, Nature ’05 Manchester+Lancaster, Nature Phys ’06

robust quantum Hall phenomena zero LL directly in the density of states room-temperature QHE 250K 150K 100K 200K B =16 T -1 1 0.4 0.6 quantum capacitance gate voltage (V) 30K gate voltage (V) xx (k) -6 2 4 -60 -30 60 30 xy (e2/h) 10 20 -4 -2 30T 300K Manchester+Columbia, Science ‘07 Manchester, PRL 2010

NEW PHYSICS ACCESS TO RELATIVISTIC-LIKE PHYSICS IN CONDENSED MATTER EXPERIMENT

EXAMPLE #1: Klein Tunnelling

Klein Tunnelling Klein 1929 Katsnelson + Manchester 2006 Falko et al 2006 Gorbachev et al, Nanolett ’08 Stander et al, PRL ’09 Young et al, Nature Phys ‘09

conductivity “without” charge carriers EXAMPLE #2: Manchester, Nature ’05

Minimum Quantum Conductivity ρmax -80 -40 80 40 Vg (V) ρ (k) 2 4 6 10K E =0 zero-gap semiconductor no localization in the peak down to 30mK and for million-range mobilities

Minimum Quantum Conductivity “quantized” conductivity NOT conductance (~e2/h per spin and valley) data from 2007 min (4e2/h) 1 1/  (cm2/Vs) 12,000 4,000 8,000 2 annealing recent samples with million mobility one electron per sample makes it a metal Fradkin 1986; Lee 1993; Ludwig 1994; Morita 1997; Ziegler 1998 … Peres 2005; Gusynin 2005; Katsnelson 2006; Tworzydlo 2006; Cserti 2006; Ostrovsky 2006 …

Minimum “Mott” Conductivity Mott’s argument: not the case of other materials NO LOCALIZATION AG & Allan MacDonald, Phys. Today 2007

fine structure constant EXAMPLE #3: visualization of fine structure constant Manchester, Science 2008

GRAPHENE OPTICS one-atom-thick single crystal visible by naked eye Manchester, Science ’08 100 µm bilayer graphene air white light transmittance (%) 98 100 96 50 25 distance (m) one-atom-thick single crystal visible by naked eye

GRAPHENE OPTICS e2 c  = coupling of light with 100 bilayer graphene air white light transmittance (%) 98 100 96 50 25 distance (m) 2.3% e2 c  = G (e2/2h)  (nm) 1.5 0.5 1.0 600 700 500 light transmittance (%) 90 theory of 2D Dirac fermions: Gusynin ‘06 Kuzmenko ‘08 80 1.5 2.0 2.5 3.0 E (eV) coupling of light with relativistic-like charges should be described by coupling constant  a.k.a. fine structure constant one-atom-thick single crystal visible by naked eye

relativistic fall on superheavy nuclei EXAMPLE #4: Shytov et al PRL 2007 Castro Neto et al PRL 2007 …..

Atomic Physics Z Z supercritical regime Positron emission slides courtesy of Antonio Castro Neto

Graphene Physics “artificial atoms” easily become overcritical Z

Manchester, Science ’09 & arxiv 2010 EXAMPLE #5: New Graphene-Based Materials Manchester, Science ’09 & arxiv 2010

Graphene as GigaMolecule both surfaces available (bi-surface chemistry; chemistry of individual gigamolecules) chemical reactions: C + X => CX

FluoroGraphene make large graphene membranes expose them from BOTH side to atomic F (using XeF2) Raman, optics, TEM, XPS, transport

FluoroGraphene make large CHANGES IN RAMAN graphene membranes expose them from BOTH side to atomic F (using XeF2) CHANGES IN RAMAN 1600 3000 1200 2600 2 intensity (a.u.) 4 6 Raman shift (cm-1) pristine D G 2D fluorographene 30h 20h XPS & EDX: C:F  1 9h 1h Raman, optics, TEM, XPS, transport

Stoichiometric Derivative fluorographene (“2D Teflon” ) optical gap of 3.0eV chemical reactions: C + F => (CF) wide-gap semiconductor chemically & thermally stable mechanically strong exposure to atomic fluorine, using XeF2

CORNUCOPIA OF NEW SCIENCE MESSAGE TO TAKE AWAY CORNUCOPIA OF NEW SCIENCE not only electronic properties but optical, mechanical, chemical, etc.

INDUSTRIAL SCALE PRODUCTION WHAT ABOUT APPLICATIONS? INDUSTRIAL SCALE PRODUCTION IS A DONE DEAL

only realistic examples APPLICATION OVERVIEW only realistic examples

EXAMPLE #1: ON SALE ALREADY

best possible TEM support conductive ink production within last 3 years: from none to >100 ton pa “multilayer graphene” AVAILABLE from Graphene Industries; Graphene Research; Graphene Supermarket

CARBON NANOTUBES OR GRAPHITE ANY APPLICATION WHERE CARBON NANOTUBES OR GRAPHITE ARE CONSIDERED can be MUCH BETTER both sides bind monolayers cannot cleave any further

EXAMPLE #2: THz Transistors

THz TRANSISTORS ballistic transport high velocity great electrostatics scales to nm sizes Y. Lin (IBM) 3 μm SiO2 Si graphene ultra high-f analogue transistors; HEMT design Manchester, Science ’04 -100 -50 100 50 Vg (V)  (k) 2 4 6 US military programs: 500 GHz transistors on sale by 2013 years demonstrated (IBM & HRL 2009): ~100 GHz even for low  & long channels

EXAMPLE #3: OPTOELECTRONICS

ULTRAFAST PHOTODETECTORS ballistic transport of photo-generated carriers in built-in electric field e h n-type doping metal p-type graphene Avouris, Nature Photo 2010 DESIRABLE TO IMPROVE: only ~2.3% conversion because a monolayer is transparent

Graphene instead of ITO EXAMPLE #4: Graphene instead of ITO

flexible: strain >15% SUBSTITUTE FOR ITO Manchester, NanoLett 2008 conductive:  <100/□ transparent: ~97% flexible: strain >15% chemically inert transparent polymer film WORKING 10 m LCD-GRAPHENE PIXEL liquid crystal active layer active layer graphene electrodes

SUBSTITUTE FOR ITO conductive:  <100/□ transparent: ~97% flexible: strain >15% chemically inert transparent polymer film  ~40/□ transparency ~90%  ~5,000 cm2/Vs Hong, Nature Nano 2010 reasonably cheap: ~$50/m2 liquid crystal active layer graphene electrodes REMAINING PROBLEM: stability of doping

Samsung Graphene Road Map: first products in 2012 TOUCH & OTHER SCREENS bendable & wearable transparent polymer film liquid crystal active layer graphene electrodes Samsung Graphene Road Map: first products in 2012

Little Considered Applications EXAMPLE #5: Little Considered Applications

ILLUMINATING WALL PAPER perfect match for organic LED transparent polymer film polymer LED graphene electrodes both anode & cathode Robinson, ACS Nano 2010

STRAIN SENSORS graphene: cheaper & larger strains SKKU + Samsung, NanoLett 2010 ~$10 each global market ~$60 billion graphene: cheaper & larger strains compatible with existing tech Samsung Graphene Road Map: production in 2014

INCREDIBLY RAPID PROGRESS: MESSAGE TO TAKE AWAY INCREDIBLY RAPID PROGRESS: AFTER ONLY 5 YEARS APPLICATIONS NO LONGER A WISHFUL THINKING only their extent remains unclear