Graphene: Experimental Overview 10 3 papers 10 2 papers Eva Y. Andrei Rutgers University Nobel Symposium Stockholm May 2010
Graphene: An Experimental overview Making graphene Gee Wizz experiments Graphene decoupled from substrate Graphene on graphite Suspended graphene
Making Graphene Exfoliation Scotch tape with graphite flakes Press Si/SiO 2 onto flakes on the tape 300 nm SiO Si Novoselev et al Science (2004) < 100 mm
Making Graphene Graphitization Epitaxial grapehene on SiC Epitaxial graohene W. A. de Heer et al (2007) C. Berger, et al J. Phys. Chem.B 108 (52) (2004) Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide K. V. Emtsev 1, et al Nature materials (2009) 2009 IEEE Epitaxial Graphene Growth on SiC Wafers D.K. Gaskill et al. 2
Making Graphene Chemical Vapor Deposition Epitaxial grapehene on metals Ir, Ru, Ni, Cu
Gee Wizz: Mechanical Young s modulus ~ 1 TPa graphene Impermeable membrane STM studies of biological assays Ultra - Filtration S. Bunch et al,nano Letters 08
Gee Wizz: Chemical Single molecule detection NO 2, NH 3, CO F Schedin et al,nature Materials 07
Gee Wizz: Optical Graphene layers change their opacity when a voltage is applied, Transmittance at Dirac point: T=1-ap =97.2% R.R. Nair et al, Science (2008). P. Blake et al, Nano Letters, 08
What is it good for? Y. M. Lin et al Science 2010 T. Mueller et al Nature Photonics 2010 TEM Imaging and dynamics of light atoms and molecules on graphene J. Meyer et al,nature 2008 (Berkeley) Bio -graphene DNA on graphene protected from break-down by enzymes. Differentiates between Single stranded and double stranded. Neuron growth enhancement Potential for Drug delivery, gene therapy Z. Tang, et al Small. (2010) (PNNA)
Electronic structure E E( k) = vf k E k y k x Dirac Point D(E) 2 1 D E) = E 2 p v ( 2 F Degeneracy = g s xg v =4 Landau Levels McLure 1956 E B 0 2 En = sgn( n) 2e vf n B D(E) Flux Degeneracy = # of flux lines n = B 0
Charge inhomogeneity (e-h puddles): x Graphene on SiO 2 SET microscopy DOS conductivity h e Martin, et.al, (2008) DV g E V gmin ~1-10V n min ~ 10 11 cm -2 (ΔE F ~30-100meV) e-h puddles z smeared Dirac point n min minimum carrier density
Graphene on SiO 2 : STM Charge inhomogeneity (e-h puddles): x di/dv (a.u.) STM topography DOS STM spectroscopy 1.0 h e 0.8 0.6 0.4 Dirac point 0.2 0.0-400 -200 0 200 Sample Bias (mv) E
Graphene on Graphite: STM STM home built Temperature T=4 (2K) Magnetic field B=13 (15T) Scan range 10-10 -10-3 m Graphite Clean Lattice matched Conductor Topography z structure Spectroscopy z Density of states B=0 Spectroscopy z Density of states B>0
STM: Graphene on Graphite di/dv (a.u.) topography B=0 spectroscopy B>0 spectroscopy Linear DOS Landau levels 0.8 0.6 0.4 skip 0.2 0.0 T 0.0-200 -100 0 100 200 Sample bias (mv)
di/dv Landau level spectroscopy G. Li, E.Y. A - Nature Physics, 3, 623 (2007) G. Li, A. Luican, E. Y. A., Phys. Rev. Lett (2009) 2.8 2.4 2.0 1-5-4-2 -1 2 3 4-3 0 10T 8T 1.6 6T 1.2 0.8 4T 2T 0T 0.4 0.0-0.2-0.1 0.0 0.1 0.2 E(meV) SiC: Miller et al Science 2009
Energy (mev) Massless Dirac Fermions G. Li, E.Y. A - Nature Physics, 3, 623 (2007) G. Li, A. Luican, E. Y. A., Phys. Rev. Lett (2009) E j = v 2e B N, N = 0, 1, 2... F 200 150 100 2 T 4 T 6 T 8 T 10 T 50 0-50 -100-150 v F = 0.8 x10 6 m/s E D = 16.6±0.5 mev -6-5 -4-3 -2-1 0 1 2 3 4 5 6 sgn(n) ( n B) 1/2
(v-v 0 )/v Graphene on graphite other results G. Li, E.Y. A - Nature Physics, 3, 623 (2007) G. Li, A. Luican, E. Y. A., Phys. Rev. Lett (2009) Electron-phonon interactions Slow down of quasiparticles 0.2 6 v F = 0.8 10 m/ s K K 0.0-0.2-0.4-0.6 e-e interactions Quasiparticle lifetime -0.8-0.6-0.4-0.2 0.0 0.2 0.4 E(eV) t qp E 1 9ps / mev Gap at Dirac point broken symmetry gap D = 2 mv F ~ 10meV skip
Quantum Hall effect in graphene on SiO 2 V g K. Novoselov et al Nature 2005 Y. Zhang et al, Nature 2005 K.S. Novoselov et al, Nature 2005
Quantum Hall Effect Number of edge modes is topological Chern number Each filled Landau level contributes g edge modes (g degeneracy) Each edge mode contributes one quantum of Hall conductance e s xy = 2 = g = g( N 4, N 1/ 2) = 2, 6 = 0, 1,.. E D(E) 14 10 6 2 0-2 s xy (e 2 /h) Single particle physics -6-10 - 14 No FQHE in graphene on SiO 2 (B< 45T) Correlation-challenge
Suspended Graphene X. Du, I. Skachako, A. Barker, E. Y. A. Nature Nanotech. 3, 491 (2008) Bolotin et al, Solid State Communications (2008) Substrate roughness Trapped charges Quench condensed ripples 2 terminal Get rid of the substrate! SiO 2 Si Hall bar L< 1 mm
Non-Suspended versus Suspended Graphene r(k ) X. Du, I. Skachko, A. Barker, E. Y. A. Nature Nanotech. 3, 491 (2008) 20 r = 1 s 20 4K Non-suspended 10 ballistic 100K 200K 250K r (k ) 10 suspended Ballistic 0-0.5 0.0 0.5 0-0.5 0.0 0.5 n(10 12 cm -2 ) n(10 12 )cm -2
Non-Suspended versus Suspended Graphene X. Du, I. Skachako, A. Barker, E. Y. A. Nature Nanotech. 3, 491 (2008) Non suspended s ~ n, l mfp << L sample n min ~ 10 11 cm -2 m ~ 10 4 cm 2 / V s 20 4K Suspended s ~ n 1/2, l mfp ~ L sample n min ~ 10 9 10 10 cm -2 m ~ 10 5-10 6 - cm 2 / V s r (k ) 10 suspended Ballistic Ballistic transport Approaching Dirac point 0-0.5 0.0 0.5 n(10 12 )cm -2
Suspended Graphene and QHE Bolotin et al, Solid State Communications (2008) 1mm Hall bar (6 lead) V d =0 V s =V H. s xy (e 2 /h) 0-2 -4-6 actually 6 2 s xy Hall conductivity expect hope fraction s 2 e s xy = 2, 6,.. = 4( N 1 ) 2 2 e Hall angle = 90 o -6-4 -2 0 The Hall-bar Standard No contact resistance Separates s xy and r xx Activation gaps works for large samples NOT for small samples Suspended Graphene: No QHE in Hall bar configuration
G(e 2 /h) QHE in 2-terminal measurement V s =V H V d =0 2 lead Hall angle = 90 o X. Du et al. Nature Nanotechnology (08) 14 c W ~ 3L D. Abanin, L. Levitov, PRB (08) 10 6 2 1T 2T 3T 4T 5T 6T 8T 10T 12T -14-10 -6-2 0
G (e 2 /h) FQHE in 2-terminal measurement X. Du, I. Skachko, F. Duerr, A. Luican, EYA, Nature 462, 192 (2009) 2 1 2T 6T 8T 12T = FQHE 0-2 -1 0-1/3 FQHE in graphene Seen already at 2T Persists up to 20K (in 12T) Bolotin et al (Columbia) Nature 462 (2009) Geim & Novoselov (Manchester)
G G(e 2 /h) 2 /h) Suspended Graphene: two terminal measurement X. Du, I. Skachko, F. Duerr, A. Luican, EYA, Nature 462, 192 (2009) 2 1 1 12T 2T 40K 20K 6T 10K 8T 4K 12T 1.2K = FQHE 1/3 0 FQHE in graphene Seen already at 2T Persists up to 20K (in 12T) -2-1 0-1 1/3 0-1/3 D ( 12T)~ 4.4K Bolotin et al (Columbia) Nature 462 (2009) D ( 12T)~ 0K Geim & Novoselov (Manchester) D. Abanin, et al, PRB (2010)
Ground state of neutral graphene in field Alicea & Fisher (2006) Normura & Macdonald, (2006) Abanin, Lee, & Levitov, (2007); Spin first D Spin > D valley Valley first D Spin < D valley Alicea & Fisher (2006) Gusynin & Sharpov (2006) = 1 valley split =+1 =+1 = 1 spin split =1 valley split Zhang et al (07) tilted field expt = 0 = = 0 = B B =0 conducting Abanin et al (07) e x e x =0 insulating Checkelsky, et al (08) Conductor QH edge states QH edge states bulk edge bulk edge Insulator
R ( ) Magnetically induced insulating phase R max ( ) X. Du, I. Skachko, F. Duerr, A. Luican, EYA, Nature 462, 192 (2009) 10 10 1T 2T 10 9 3T 4T 5T 4.2K 10 8 6T 8T 10T 12T 10 7 10 6 10 5 <0.1 B>1T -0.3-0.2-0.1 0.0 0.1 0.2 0.3 R max ~ R e ( T*/ T ) 1/ 2 T*(4T)~ 100K 0 10 8 12T 10T 8T 10 7 6T 10 6 10 5 10 4 5T 3T 2T 1T 0.1 0.2 0.3 0.4 0.5 T -1/2 Insulating phase Spin polarized bulk + broken edges Correlated electron state: bulk antiferromagnet+no edge states CDW or SDW
Supended CVD Graphene membrane Energy (mv) with: A. Reina, J. Kong (MIT) R. R. Nair, K. Novoselov, A. Geim (Manchester) SEM 50 mm optical micrograph STM- Landau levels 200 100 B=3 T 4.4 K 0 v F =1.16x10 6 m/s -100-2 -1 0 1 2 n 1/2
Twisted graphene Twist between top layers z Moiré pattern θ=3 θ=0 θ=4 θ=6 θ=10 Period of superstructure : a0 2.46 Å Lopes dos Santos et al PRL 99, 256802 (2007).
STM topography: Moiré pattern Moiré on graphite superstructure surface G. Li, et al Nature Physics (2010) superstructure L=7.5nm q=.79 o x4 x250 M1 G M2 Boundary of area with superstructure G
di/dv (a.u.) Spectroscopy Moiré pattern Van on Hove graphite surface singularities G. Li, et al Nature Physics (2010) M 2 2.0 M 1 1.5 M 2 G 1.0 G 0.5 0.0 M 1-200 0 200 sample bias (mv) G M 2 M 1 Two peak structure only in twisted region
Electronic dispersion of twisted layers PRL 99, 256802 (2007). ΔE DK 2K sin( q / 2) DK = S. Shallcross, et al 2009 G. Mele PRB 2010 Bistrizer, MacDonald 2010
Van Hove singularities G. Li et al. Nature Physics 6, p109 (2010) ΔE Density ΔE of states Twisted graphene develops strong Van Hove singularities
Van Hove singularities di/dv (a.u.) G. Li et al. Nature Physics 6, p109 (2010) ΔE Density ΔE of states 2.0 D=90 mev, q=.79 o 1.5 1.0 0.5 0.0-0.2-0.1 0.0 0.1 0.2 sample bias (ev)
Van Hove singularities G. Li et al. Nature Physics 6, p109 (2010) ΔE Density ΔE of states Twist engineering of electronic DOS
Summary di/dv (a.u.) di/dv (a.u.) di/dv (a.u.) G (e 2 /h) Gee Wizz Mechanical ultra-strong, impermeable Chemical ultra-sensitive nose Optical gate controlled transmittance Graphene on graphite Honeycomb structure Dirac fermions Linear Density of states Well defined Dirac point Direct observation of Landau levels 0.8 0.6 0.4 0.2 0.0 0.0 T -200-100 0 100 200 Sample bias (mv) 1.0 0.8 0.6 0.4 0.2 0.0 m 0 H = 4 T T=4.36 K D: (140,116) spi20182 D = 2. mev -200-100 0 100 200 sample bias (mv) Suspended graphene 2 2T 6T 8T 12T Exfoliated membranes Ballistic transport on micron length scales Fractional quantum Hall effect 1 0-2 -1-1/3 0 SKIP CVD membranes Twist control of electronic properties 2.0 1.5 1.0 0.5 0.0-0.2-0.1 0.0 0.1 0.2 sample bias (ev)
Thanks Xu Du Ivan Skachko Guohong Li Adina Luican Anthony Barker Patrick Stanger Fabian Duerr Justin Meyerson Collaborators: MIT: J. Kong, A. Reina Manchester: A. Geim, K. Novoselov, R. Nair Porto: J. los Santos BU: A.H. Castro Neto Princeton: D. Abanin MIT: L. Levitov