Quantum Transport in Graphene

Bernard Plaçais

d h i é i (MESO)groupe de physique mésoscopique (MESO)

Laboratoire Pierre Aigrain, Ecole Normale Supérieure, Paris

GDR physique quantique mésoscopique (http://www.gdr-meso.phys.ens.fr)

Collaborators : E. Pallecchi, A. Betz, J.-M. Berroir, G. Fève, G. Glattli, T. Kontos.

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« Electric Field Effect in Atomically Thin Carbon Films »

GDRI-GNT, Dourdan, 10 février 2011 2(K. Novoselov et al., Science 2004)

Suspending graphene (2008)

(Temperature dependent transport in suspendedgraphene, K.I. Bolotin et al. PRL2008)

Wh t th fi i t f Di f i ?What are the fingerprints of Dirac fermions ?What limits mobility ?Why a non-zero conductivity minimum ?

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Why do we need quantum transport ?

Comparison with the 2DEG paradigm

GaAs mobility, Pfeiffer et al.

Suspended graphene (2008)

Graphene on h-BN (2010)

Graphene on SiO2 (2004)Graphene on SiO2 (2004)

Are Dirac fermions useful for something ?

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Are Dirac fermions useful for something ?

content

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Doped graphene

hole doped neutral electron doped

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Low energy : semi-metal

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(Colloquium ; The transport properties of graphene: An introduction, N.M.R. Peres RMP 2010)(Electronic transport in two dimensional graphene, S. Das Sarma et al. RMP2011)

Ultra relativistic Dirac Fermions

t bl tti ( i i ti l !!) two sublattices (spinor is essential !!)

two valleys (more like a complication)

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electronic properties

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Scattering of Dirac fermions

qinitial

qfinal

qinitial

GDRI-GNT, Dourdan, 10 février 2011 10(Ecole GDR Graphene, J.N. Fuchs, Cargèse, 12-22 octobre 2010)

Disorder classified according to symetry (intravalley)

how to identify these exotic scattering mechanisms ?

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(e.g. : Properties of graphene: a theoretical perspective, Abergel, Advances in Physics 2010)

Density dependence of conductivity

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(Ecole GDR Graphene, J.N. Fuchs, Cargèse, 12-22 octobre 2010)(Electronic transport in two dimensional graphene, S. Das Sarma et al. RMP2011)

Comparison with elastic scattering time

comparison with quantum scattering time favors resonnant scattering

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(Transport and Elastic Scattering Times as Probes of the Nature of Impurity Scattering …. , Monteverde et al. PRL2010)

comparison with quantum scattering time favors resonnant scattering

compressibility and gate conductance (RF transport)

See POSTER Emiliano Pallecchi !

GDRI-GNT, Dourdan, 10 février 2011 14(Transport scattering time probed through rf admittance of a graphene capacitor, Pallecchi et al., PRB 2011)

compressibility and gate conductance (RF transport)

GDRI-GNT, Dourdan, 10 février 2011 15(Transport scattering time probed through rf admittance of a graphene capacitor, Pallecchi et al., PRB 2011)

outline

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When do we need quantum transport ?

L>>L

conductance = electronic wave transmission

quantum tunneling is important (tuneable wave length/transmission)

interference effects, quantum noise ,…..

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, q ,

Landauer-Büttiker scattering approach

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(Shot noise in mesoscopic conductors, Blanter-Büttiker, Physics Reports 2000)

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Evanescent waves at D-point : ballistic case

Fano factor is 1/3 at neutrality

Conductance minimum

y

(Sub-Poissonian Shot Noise in Graphene Tworzydlo PRL 2006) ( Shot noise in ballistic graphene, Danneau et al., PRL 2008)

Transport is virtually noiseless in doped graphene (F<<1)

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(Sub Poissonian Shot Noise in Graphene, Tworzydlo PRL 2006)

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( Shot noise in ballistic g aphene, anneau et al., 008)

Zener-Klein tunneling neutrality: non linear I-V

(thesis N Vandecasteele UPMC 2010)

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(Current-voltage characteristics of graphene devices: Interplay between Zener-Klein tunneling and defects,Vandecasteele et al. PRB 2010)

(Graphene field-effect transistors based on boron nitride gate dielectrics, I. Meric et al., arXiv:1101.4712v1)

(thesis, N. Vandecasteele, UPMC 2010)

Ballistic p-n-p Fabry-Pérot interferometer

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(Ecole Cnano Tremblay, P. Kim 2009, Young and Kim, Nature Phys. 2009)

Ballistic p-n-p Fabry-Pérot interferometer : Berry phase

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(Ecole Cnano Tremblay, P. Kim 2009, Young and Kim, Nature Phys. 2009)

Contents

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Graphene microwave transistors : MOG-FETs

IEMN-LEM-2009

IBM-2010

Lin et al., Science 327, 662, 2010F. Schwierz, Nature Nanotech. 2010

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Large scale graphene nanoribbon RF transistors

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(60 GHz current gain cut-off frequency graphene nanoribbon FET, N. Meng et al., Int. J. of Microwave and Wireless Technologies, 2010)

Ballistic MOG-FETs ? : graphene on h-BN (2010)

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(Graphene field-effect transistors based on boron nitride gate dielectrics, I. Meric et al., arXiv:1101.4712v1)

D-fermion optics (futurist view ?)

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(The Focusing of Electron Flow and a Veselago Lens in Graphene p-n Junctions, V. Cheianov et al., Science 2007)

conclusions

• Dirac fermions are qualitatively different from light electrons in 2DEGsq y g

• Density of state effects (DOS-cones) are prominent

• Sublattice pseudo-spin (Dirac-spinors) description is essential

• Quantum tunneling rules transport at neutrality (Zener-Klein tunneling)

• Dirac-fermions are best exploited in the ballistic regime

M t l O id G h t i t (MOG FET ) f i• Metal-Oxide-Graphene transistors (MOG-FETs) for microwave sensors

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