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 »
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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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