Graphene bipolar heterojunctions SD LG V BG C BG C LG V LG V SD -Density in GLs can be n or p type -Density in LGR can be n’ or p’ type We expect two Dirac minima! V BG (V) G (e 2 /h) V LG = -10 V Related work by Huard et al. PRL (2007) EL LG GLs Local Gate Region 1  m Oezyilmaz, Jarrilo-Herrero and Kim PRL (2007)

Graphene heterojunction Devices n np x potential n nn’ x potential p pp’ x potential p pn x V LG (V) V BG (V) G (e 2 /h) 10 n-n’-n p-n’-p p-p’-p n-p’-n pp n’ V BG (V) G (e 2 /h) 1  m

Ballistic Quantum Transport in Graphene Heterojunction n np x potential Graphene NPN junctions Novoselov et al, Nat. Phys (2006) Klein Tunneling Transmission coefficient T tot n p =1x10 12 cm 2 n p =3x10 12 cm 2 n n =0.5x10 12 cm 2  Collimation: (resonance) k 2x =  n/L Perfect transmission

Realistic Graphene Heterojunction Requirements for Ballistic pn junctions Long Mean free path -> Ballistic conduction Large electric field -> Small d -> promote resonance Smooth electrostatic n ~ cm -2 F ~ 30 nm d dielectric ~ 20 nm L ~ 100 nm transmission T  Tunneling through Classically Forbidden regime T Cheianov and Fal’ko (2006) Zhang and Fogler (2008) Tunneling through smooth pn junction Strong forward Collimation! graphene electrode 1  m SEM image of device 20 nm Mean free path ~ 50 nm Mean free path < 100 nm

Transport Ballistic Graphene Heterojunction V BG = 90 V V BG = -90 V ppp pnp npn nnn graphene electrode 1  m Young and Kim (2008) V TG (V) Conductance (mS) PN junction resistance Cheianov and Fal’ko (‘06) 18 V -18 V ´´  L n 1,, k 1, T T T R R* n 1,, k 1, n 2,, k 2 Conductance Oscillation: Fabry-Perot k 1 /k 2 = sin  ’ / sin   = 2L /cos  ’ See also Shavchenko et al and Goldhaber-Gordon’s recent preprint

Quantum Oscillations in Ballistic Graphene Heterojunction n top (10 12 cm 2 ) n back (10 12 cm 2 ) dR/dn top ( h/e cm -2 ) Resistance Oscillations ´´  L n 1,, k 1, T T T R R* n 1,, k 1, n 2,, k 2 Magnetoresistance Oscillations (B=0) Aharonov-Bohm phase:  B =B L 2 sin  ’/cos  ’ V T (V) B (T) 0 1 dG/dn top (e 2 /h cm -2 )  (V B =-50 V) )

Resonant Magneto-Oscillations in Graphene Heterojunctions Exp Theory Two fitting parameters: l LGR = 27 nm; l GL = 50 nm Ballistic pn junction Collimation See also Shytoy et al., arXiv:

Graphene Electronics Conventional Devices Cheianov et al. Science (07) Graphene Veselago lense FET Band gap engineered Graphene nanoribbons Nonconventional Devices Trauzettel et al. Nature Phys. (07) Graphene psedospintronics Son et al. Nature (07) Graphene Spintronics Graphene quantum dot (Manchester group) Many body & correlated effect to come!

Conclusions Carbon nanotube FET is mature technology demonstrating substantial improvement over Si CMOS Controlled growth and scaling up of CNTFET remains as a challenge Graphene provides scaling up solution of carbon electronics with high mobility Controlled growth of graphene and edge contol remains as a challenge Novel quantum device concepts have been demonstrated on graphene and nanontubes

Acknowledgement Meninder Purewal (nanotube) Kirill Bolotin (suspended graphene) Melinda Han (nanoribon) Dmitri Efetov (graphene heterojuncton) Andrea Young (graphene heterojunction) Barbaros Oezyilmaz (now at NSU) Pablo Jarrilo-Herrero (now at MIT) Funding: Collaboration: Horst Stormer Kim Group Picnic: 2008 Central Park, New York

T -1 ln(R) Arrhenius plot Variable Range Hopping in Graphene Nanoribbons Conductance (  S) V g (V) W = 37 nm K 15K 100K 200K 300K E x EFEF d: dimensionality 70 nm 48 nm 37 nm 22 nm 15 nm 31 nm ln(R) T -1/3 70 nm 48 nm 37 nm 22 nm 15 nm 31 nm 2D VRH ln(R) T -1/2 70 nm 48 nm 37 nm 22 nm 15 nm 31 nm 1D VRH T

Graphene Quantum Hall Edge State Conduction EL LG GLs Local Gate Region 1  m simple model (following Haug et al) Oezyilmaz, et al., PRL (2007) See also Related work by Williams et al. Science (2007)

Temperature Dependent Oscillations Conductance (mS) V TG (V) V BG = 90 V npn nnn V