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some things you might be interested in knowing about Graphene

some things you might be interested in knowing about Graphene. FEW EXAMPLES OF MOST RECENT WORK @ MANCHESTER. Serge Morozov unpublished. Physics at the Dirac Point (Lifshitz transition in bilayer). suspended devices. 2  m. 2 K. resistivity (k). 20. 5 K. 10. Temperature.

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some things you might be interested in knowing about Graphene

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  1. some things you might be interested in knowingabout Graphene

  2. FEW EXAMPLES OF MOST RECENT WORK @ MANCHESTER

  3. Serge Morozov unpublished Physics at the Dirac Point (Lifshitz transition in bilayer)

  4. suspended devices 2 m 2 K resistivity (k) 20 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 concentration (1010 cm-2) transport mobilities > 1,000,000 cm2/V·s remnant doping < 109 cm-2 SdH oscillations start < 100G quantum mobilities > 1,000,000 cm2/V·s level degeneracy lifted < 0.1T

  5. suspended devices 2 m 800 T = 2K 600 B=0.5T R (k) 400 resistivity (k) 200 zero B 20 0 -2 -1 0 1 2 n (1011cm-2) 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 concentration (1010 cm-2) GAP IS OPEN BY MAGNETIC FIELD for some devices <1T (VALLEY GAP?)

  6. suspended devices 2 m resistivity (k) 20 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 concentration (1010 cm-2) fractional QHE need 4-probe devices ! Manchester, unpublished first reported by Andrei’s group, Nature ’09 Kim’s group, Nature ’09; Lau’s group, arxiv 2010 million mobilities but the quality of quantization remains really bad

  7. suspended devices 2 m 14 16  (k) T = 2K 12 zero B 10 -5 0 n (108cm-2)  (k) 8 resistivity (k) 4 20 0 -2 -1 0 1 2 n (1011cm-2) 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 concentration (1010 cm-2) remnant doping < 109 cm-2 ~T continues sharpening below 1K charge inhomogeneity < 108 cm-2 can smoothly pass from one electron to one hole Fermi energy scale < 1 meV

  8. 2 2 monolayers maximum resistivity (h/4e2) 1 resistivity (k) 20 2 bilayers 0 0 50 100 150 200 T (K) 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 concentration (1010 cm-2) PROBING DIRAC POINT • NO ENERGY GAP • NO METAL-INSULATOR • TRANSITION • even with one electron per device resistivity @ Dirac point   T approaches T=0 approx. linearly monolayer: min  moves closer to 4e2/h bilayer: min  remains > 4e2/h

  9. PROBING DIRAC POINT MONOLAYER: gradual gap opening BILAYER: more complex behavior

  10. B =0.25 T ~3x109 cm-2 12 8  (k) 15  (k) magnetoresistance at Dirac point 5 PROBING DIRAC POINT BILAYER: more complex behavior  =4 energy gap induced by gate is less than T  =-4

  11. 10 thermal broadening 150 K  - min/e (109 cm-2) 100 K 5  (k) 50 K 20 5 K 0 -10 0 10 gate-induced concentration (109 cm-2) 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 n (1010 cm-2) PROBING DIRAC POINT first, let us analyze monolayer total concentration near Dirac point, curves collapse on a universaldependence measure concentration of thermally excited carriers

  12. 1 thermalcarriers (1010 cm-2) thermal broadening .5 0  (k) 0 50 100 150 200 T (K) 20  T 2 monolayer 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 n (1010 cm-2) PROBING DIRAC POINT first, let us analyze monolayer number of carriers at energy ~kT

  13. 20  T bilayer thermal carriers (1010 cm-2) thermal broadening 10  T 2 monolayer 0 0 50 100 150 200 T (K) PROBING DIRAC POINT number of carriers at energy ~kT  (k) 20 5 K 10 Temperature 200 K 0 -10 -5 0 5 10 n (1010 cm-2)

  14. 3 bilayer 2 thermal carriers (1010 cm-2) 1 ~3x109 cm-2 0 0 10 20 30 T (K) PROBING DIRAC POINT number of carriers at energy ~kT thermal broadening DENSITY DIMINISHES  (k) 20 5 K 10 Temperature like a gap ~1 meV at the Dirac point but with a finite T-dependentDOS within the gap 200 K 0 -10 -5 0 5 10 n (1010 cm-2)

  15. 3 bilayer 2 thermal carriers (1010 cm-2) 1 ~3x109 cm-2 0 0 10 20 30 T (K) PROBING DIRAC POINT number of carriers at energy ~kT thermal broadening DENSITY DIMINISHES  (k) 20 5 K 10 Temperature like a gap ~1 meV at the Dirac point but with a finite T-dependentDOS within the gap 200 K 0 -10 -5 0 5 10 n (1010 cm-2)

  16. 3 bilayer 2 thermal carriers (1010 cm-2) ~1 meV 1 ~3x109 cm-2 0 0 10 20 30 T (K) PROBING DIRAC POINT number of carriers at energy ~kT thermal broadening  (k) 20 5 K 10 Temperature like a gap ~1 meV at the Dirac point but with a finite T-dependentDOS within the gap 200 K 0 -10 -5 0 5 10 n (1010 cm-2)

  17. PROBING DIRAC POINT cyclotron gaps between different Landau levels 0.026m0 OPEN FOR INTERPRETATION one of many possibilities: symmetry-breaking e-e phase transition Falko’s group arxiv 2010 gap between zero and first LL does not want to close with decreasing B down to 500G

  18. MESSAGE TO TAKE AWAY LIFSHITZ TRANSITION MODIFIED BY SOMETHING(?) DIRAC POINT PHYSICS IS ACCESSIBLE TO STUDIES IN ALL DETAILS million mobilities in 4-probe geometry should bring a lot more of new physics

  19. Leaving the Carbon Flatland vertical transport through one-atom-thick crystals Peter Blake unpublished

  20. Many Other 2D Materials Possible 2D NbSe2 in AFM 2D boron nitride in AFM 0Å 9Å 16Å 23Å 0Å 8Å 23Å 1m 0.5m 1m 1 m 1 m 2D Bi2Sr2CaCu2Ox in SEM 2D MoS2 in optics SOME ARE INSULATORS Manchester, PNAS 2005

  21. tunneling devices superconducting junctions S S one-atom-thick barriers? atomically smooth and continuous (impossible by MBE) resonant tunneling devices spin tunneling devices

  22. 2D CRYSTALS AS TUNNEL BARRIER Au Au boron nitride 1 layer BN top Au contact Au contact can now find BN monolayers in an optical microscope 2m

  23. MONOLAYER BARRIER height: gap ~5eV effective thickness ~5-6Å 1 80 resistivity ~1 Mm2 resistivity ~1 km2 0.5 40 Au Au tunnel current (A) 0 tunnel current (A) 0 0.4 2 0.4  (1/k) breakdown 2 V/nm  (1/M) -0.5 0.2 -40 0.2 0 -0.4 0 0.4 voltage -0.1 0 0.1 -1 voltage tunnel current (A) -0.5 -0.25 0 0.25 0.5 0 -80 1 -0.2 -0.1 0 0.1 0.2 voltage (V) I (A) voltage (V) 0.1 exponential dependence -0.2 0.01 3.5 4.0 4.5 voltage -0.4 -5 0 5 voltage (V) trilayer 7-layer BN monolayer NO pin holes NO temperature dependence except for Zero Bias Anomaly

  24. MESSAGE TO TAKE AWAY NEW VENUE: ATOMICALLY SMOOTH, CONTINUOUS ONE-, TWO, FEW-ATOM-THICK TUNNEL BARRIERS (beyond MBE; any surface) LAYER-BY-LAYER CONSTRUCTION OF VARIOUS TUNNELING DEVICES & QUANTUM WELLS

  25. Pseudo-Magnetic Fields by Strain Paco Guinea, M. Katsnelson & AKG Nature Phys 2010

  26. Electronic Properties under Strain elastically stretched by > 15% Manchester+Cambridge, PRB 2009; Small 2009 Hone’s group, PNAS 2009 band structure changes little no gap expected even at 25% stretch Castro Neto, PRB 2009

  27. B+ B- Non-Uniform Strain non-uniform strain causes pseudo-magnetic field Manchester, PRL 2006 practically always rippled

  28. counter propagating edge currents insulating bulk K’ K Creating Uniform Pseudo-Magnetic Field [001] [010] UNIFORM FIELD graphene rectangular graphene disk [100] STRAIN ONLY field of 10T: 10% strain in m samples Nature Phys 2010; PRB 2010

  29. Giant Pseudo-Magnetic Fields strained graphene bubbles on Pt surface M. Crommie’s group, Science 2010 equivalent to magnetic fields of ~400T

  30. MESSAGE TO TAKE AWAY Strain Engineering Can Open Really Large Gaps Pseudo-Magnetic field can be UNIFORM: Landau quantization and QHE in zero magnetic field

  31. Magneto Oscillations in Quantum Capacitance Leonid Ponomarenko arxiv & PRL 2010

  32. 100 m 10 nm aluminium oxide Au/Ti Al (top gate) SiO2/insulating Si graphene Capacitance Measurements  ~10,000 cm2/Vs QUALITATIVE OBSERVATIONS: Chen & Appenzeller 2008 Xia et al Nature Nano 2009 Giannazzo at al NanoLett 2009

  33. 100 m 10 nm aluminium oxide Au/Ti Al (top gate) SiO2/insulating Si graphene Capacitance Measurements  ~10,000 cm2/Vs saturates to classical value Coxide sharpness of the dip is determined by vF QUALITATIVE OBSERVATIONS: Chen & Appenzeller 2008 Xia et al Nature Nano 2009 Giannazzo at al NanoLett 2009

  34. 100 m 10 nm aluminium oxide Au/Ti Al (top gate) SiO2/insulating Si graphene Capacitance Varies with Concentration  ~10,000 cm2/Vs saturates to classical value Coxide sharpness of the dip is determined by vF smearing n 5·1011 cm-2 vF  1.1(±0.1)·106 m/s QUANTITATIVE AGREEMENT

  35. 0.6 T =10 K B =16 T 250K 0.40 200K C (F/cm2) C (F/cm2) 12T 150K 8T 100K 0.35 0.4 30K 4T B =0T -1 0 1 -1 0 1 V V (V) (V) top gate top gate Magneto Capacitance Oscillations pronounced magneto-oscillations easily survive to room T

  36. MESSAGE TO TAKE AWAY Quantum Capacitance is a Huge Effect in Graphene Landau Quantization Survives at Room T in Modest Fields (unlike transport, this does not require >30T)

  37. CONCLUSION GRAPHENE IS A GOLD MINE FOR NEW SCIENCE & APPLICATIONS does NOT feel at all like a mature research area MUCH MORE TO COME

  38. Rahul Nair Irina Grigorieva Kostya Novoselov Misha Katsnelson (Nijmegen) Sergey Morozov (Chernogolovka) D. Elias L.Ponomarenko A. Castro Neto (Boston) F. Schedin P. Blake A. Ferrari (Cambridge) Nuno Peres (Porto), Paco Guinea (Madrid), Leonid Levitov (Boston), Rui Yang, Volodya Fal’ko (Lancaster), Soeren Neubeck, Ernie Hill, Sasha Grigorenko graphene reviews: Nature Mat ‘07; RMP ’09; Science ‘09

  39. “graphene dreams”: substitute for Si Manchester, Science 2004 de Heer et al, J.Phys.Chem. 2004 see also Dresselhaus 1996

  40. GRAPHENE ELECTRONICS 6 SiO2 4 (k) Si graphene 2 0 -100 -50 0 50 100 Vg (V) ballistic transport on submicron scale, high velocity, great electrostatics, scales to nm sizes BUT no pinch off

  41. 10 nm GRAPHENE NANO-CIRCUITS E = vF h/2D e-b lithography not 1/D2 as for electrons but much larger 1/D as for slow photons

  42.  few nm 300 K 6 (S) 10 nm 4 2 0 0 0.2 0.4 gate (V) GRAPHENE NANO-CIRCUITS stable and robust down to a few nm in size sustains large (~1 A per atom) currents E = vF h/2D e-b lithography Manchester, Science ‘08 also, Dai et al, Science ‘08

  43.  1-10 nm 300 K 6 (S) 10 nm 4 10 nm 2 0 0 0.2 0.4 gate (V) GRAPHENE NANO-CIRCUITS stable and robust down to a few nm in size sustains large (~1 A per atom) currents top-down molecular electronics PROBLEM: no tools to sculpture at true nm scale (same for any other nanoelectronics approach)

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