Download ue mesoscopique - Université Paris-Sud

Organisateurs :
Mark GOERBIG
LPS, Orsay
Gilles MONTAMBAUX
LPS, Orsay
Quantum electrodynamics in a pencil trace
K. Novoselov,
School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
When one writes by a pencil, thin flakes of graphite are left on a surface. Some of them are only one angstrom thick and can
be viewed as individual atomic planes cleaved away from the bulk. This strictly two dimensional material called graphene
was presumed not to exist in the free state and remained undiscovered until the last year. In fact, there exists a whole class of
such two-dimensional crystals. The most amazing things about graphene probably is that its electrons move with little
scattering over huge (submicron) distances as if they were completely insensitive to the environment only a couple of
angstroms away. Moreover, whereas electronic properties of other materials are commonly described by quasiparticles that
obey the Schrödinger equation, electron transport in graphene is different: It is governed by the Dirac equation so that charge
carriers in graphene mimic relativistic particles with zero rest mass.
Flat Graphene sheets made by reverse exfoliation process
V. Huc1, N. Bendiab2 T. Ebbesen3, and V. Bouchiat4,
1IPCMO-CNRS,
Orsay , 2LSP-U. Joseph Fourier, Grenoble, 3U. Louis Pasteur, Strasbourg, 4Institut Néel, CNRS-Grenoble
We present a new method to fabricate flat and large n-graphene samples.
The process is based on a reverse exfoliation method reminiscent to what is done in the smart-cut process [1] used for
Silicon-on-Insulator preparation. A freshly cleaved bulk HOPG sample is glued upside down on a silicon wafer using epoxy
mixture. After glue drying, the HOPG sample is then removed using a scalpel cut, leaving a thin graphite layer on the
substrate. Finally the multilayer is stripped down to the few layer thickness using the well-known scotch tape exfoliation
method [2]. Since the graphene flakes are firmly bond to the substrate during the exfoliation process, the obtained graphene
islands are remarkably flat and present very few folds and pleats.
The obtained n-Graphene samples are characterized using complementary probes : qpatially resolved Micro-Raman
Spectroscopy, Atomic and Electrostatic Force Microscopies and Electron transport. Signature of the high occurrence of large
single layer graphene sheets is assessed by AFM microscopy [2], together with the observation of the well characterized GBand Frequency shift [3,4] in the Raman spectra.
[1] M. Bruel et al., Jpn. J. Appl. Phys. 36, 1636 (1997), B Aspar, M Bruel, T Poumeyrol - US Patent 7,067,396.
[2] K.S. Novolesov, Science 306, 666 , (2004).
[3] A. Gupta et al., Nano letters 6, 2667, (2006).
[4] A. C. Ferrari et al., Phys. Rev. Lett. 97, 187401 (2006).
Transport et structure du graphène épitaxié
Claire Berger
CNRS-Institut Néel, Grenoble et Georgia Institute of Technology, Atlanta-USA
Nous montrons que l’on peut faire croître couches de graphène à la surface de substrats monocristallins de carbure de
silicium hexagonal 4H ou 6H. Les caractéristiques structurales et les propriétés de transport seront discutées. Les couches
peuvent être produites à grande échelle et se prêtent aisément aux analyses structurales et aux techniques conventionnelles de
lithographie.
Au niveau du transport, la magnétorésistance des couches de graphène épitaxié montre des caractéristiques attendues pour du
graphène avec une phase de Berry anormale et de l’anti-localisation. Les niveaux d’énergie de Landau présentent la
dispersion en champ du graphène. Les films ont une grande longueur de cohérence de phase électronique et une mobilité
jusqu’à 30 000cm2/Vs, qui dépend peu de la température. Les études structurales montrent que les couches ne sont pas des
films minces de graphite et que les différents plans de graphène sont désorientés. On s’attend alors à retrouver les
caractéristiques de plans isolés de graphène.
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Structure electronique du graphene en epitaxie sur sic
F. Varchon, B.Ngoc Nguyen ,C. Naud, P. Mallet, J.Y. Veuillen, C. Berger et L. Magaud
Institut NEEL/CNRS-UJF, BP166 38042 Grenoble Cedex 9, France
Récemment, de nouvelles mesures de transport électronique, effectuées sur des couches minces de graphite, ont
motivé de nombreuses équipes à s’intéresser au graphène [1] [2]. Ce système, qui est la forme cristalline bidimensionnelle du
carbone, est obtenu expérimentalement par deux méthodes. La première consiste à exfolier mécaniquement du graphite et à
déposer le ou les plans obtenus sur un substrat de type SiO2, tandis que, dans la seconde, le graphène est obtenu par recuit de
la surface du SiC 4H ou 6H.
Dans ces deux cas, les mesures de transport mettent en évidence des propriétés remarquables comme une grande
longueur de cohérence de phase ou un effet Hall quantique demi-entier. Pour ces deux systèmes, l’influence du substrat sur
les propriétés électroniques, comme par exemple un éventuel dopage, reste à évaluer.
Le système que l’on étudie se compose de un, deux ou trois plans de graphène en épitaxie sur une surface de SiC,
terminé Si ou C. Nous avons mis en évidence, via des calculs ab initio (DFT/GGA, code VASP) deux propriétés très
intéressantes de cette interface [3]. D’une part l’existence d’un plan de carbone « tampon », de structure cristalline
hexagonale semblable au graphène isolé, mais qui perd la structure électronique de type « cône de Dirac » de ce dernier. Ce
plan « tampon » passive la surface du SiC et permet donc aux plans de carbone, disposés au-dessus, d’adopter la structure
électronique de type graphène/graphite. Ces résultats sont cohérents avec les mesures STM [4]. D’autre part nous avons
montré l’existence d’un transfert de charges dépendant de la géométrie de l’interface. Ce dernier engendre un dopage des
plans de carbone et l’ouverture d’un gap aux points K de la première zone de Brillouin dans le cas de trois plans (plan
« tampon » + 2 plans de type graphène) présents sur la surface.
De plus nous nous intéressons à la structure cristallographique du premier plan de carbone épitaxié sur le SiC(0001),
appelé « nanomesh » dans la littérature [5], et qui présente une reconstruction de surface de type 6X6 observée en STM [4].
Un calcul ab initio de convergence ionique effectué sur une très grande maille (1216 atomes) composée de 2 plans de
carbone sur SiC(0001) nous permet d’analyser la géométrie de cette reconstruction.
[1] C. Berger et al, Science Vol 312, 1191 (2006)
[2] K.S. Novoselov et al, Nature Vol 438, 197 (2005)
[3] F. Varchon et al., cond-mat/0702311, soumis à PRL
[4] P. Mallet et al., cond-mat/0702406, soumis à PRL
[5] W. Chen et al., Surf. Science 596, 176 (2005)
Etats électroniques du graphène épitaxié sur SiC sondés par STM
P. Mallet, F. Varchon, C. Naud, L. Magaud, C. Berger et J.Y. Veuillen
Institut NEEL/CNRS-UJF, BP166 38042 Grenoble Cedex 9, France
Nous présentons des mesures de microscopie à effet tunnel (STM) effectuées sur un substrat 6H-SiC(0001) dont la surface a
été enrichie en carbone par sublimation du silicium, conduisant à la formation de 1 à 2 plans de graphène en surface. Ces
plans sont séparés du SiC par un plan tampon riche en C, qui n’a pas la structure du graphène, et qui joue un rôle essentiel
dans le découplage électronique graphène-substrat. En analysant le contraste des images à résolution atomique, nous
démontrons la présence en surface de deux types de terrasses (baptisées M et B), que nous pouvons attribuer sans ambiguïté
au monoplan et au biplan de graphène sur le plan tampon [1]. L’imagerie des terrasses M montre que le STM est sensible aux
états électroniques du graphène mais également à des états électroniques localisés à l’interface (dans le plan tampon). Ces
états sont probablement liés à la présence de liaisons pendantes résiduelles du plan d’interface, comme le suggèrent des
calculs ab initio réalisés dans notre groupe [2]. Nos mesures montrent qu’au voisinage du niveau de Fermi, les états
électroniques du graphène ne sont quasiment pas couplés à ces états d’interface, en excellent accord avec de très récentes
mesures de photoémission sur le même système [3]. Enfin, nous avons mis en évidence des interférences quantiques
générées par la diffusion élastique des électrons de la surface sur des impuretés présentes sur les terrasses M ou B. Ces
interférences quantiques sont directement reliées à la topologie de la surface de Fermi du monoplan ou biplan de graphène
[1].
[1] P. Mallet et al., cond-mat/0702406, soumis à PRL
[2] F. Varchon et al., cond-mat/0702311, soumis à PRL
[3] A. Bostwick et al., Nature Physics 3, 36 (2007)
Mesoscopic transport in graphene
B. Trauzettel,
Departement Physik und Astronomie, Universität Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
Two recent experiments have discovered that the conductivity of graphene (a single atomic layer of carbon) tends to a
minimum value of the order of the quantum unit e^2/h when the concentration of charge carriers tends to zero. This quantumlimited conductivity is an intrinsic property of two-dimensional Dirac fermions (massless excitations governed by a
relativistic wave equation), which persists in an ideal crystal without any impurities. In the absence of impurity scattering,
and at zero temperature, one might expect the electrical current to be noiseless. In contrast, we show that the minimum in the
conductivity is associated with a maximum in the Fano factor (the ratio of noise power and mean current).
The Fano factor at zero carrier concentration takes on the universal value 1/3 for a wide and short graphene strip. This is
three times smaller than the Poissonian noise in a tunnel junction and identical to the value in a disordered metal. We discuss
the relation of this result to the phenomenon of zitterbewegung which is present for free Dirac fermions but absent for free
Schroedinger fermions.
Work done in collaboration with C.W.J. Beenakker, Ya.M. Blanter, A.F. Morpurgo, A. Rycerz, M. Titov, and J. Tworzydlo.
Coherent transport in epitaxial graphene nano-wires
L.P. Lévy and C. Naud,
Institut Néel CNRS and Univ. J. Fourier, BP 166, 38042 Grenoble Cedex 9
Claire Berger, Xuebin Li, ZhiMin Song, Walt A. de Heer
School of physics, Giorgia Institute of Technology, Atlanta, 30332-0430, USA
Below 200K, the resistance of on patterned epitaxial multilayers graphene nanowires drops to the ballistic limit. This quasiballistic behaviour of the sample studied is explored through its mesoscopic signatures. The magneto-conductance is
dominated by slow nearly periodic oscillations and fast aperiodic conductance fluctuations of amplitude $\frac{e^2}{2h}$
satisfying Onsager-B\"{u}ttiker symmetry relations. The power spectrum and the auto-correlations functions of the
conductance fluctuations have the typical features of ballistic billiards. Their amplitude appears to be limited by
$L_T=\frac{\hbar v_0}{\pi k_{\rm B}T}$, as in quasi 1D Luttinger liquids, and exceeds several microns at 4.2K. A model
based on Büttiker multi-terminal description for imperfect quantum Hall quantization in quantum Hall systems can be used to
describe the quantum transport in this nearly-ballistic system.
The proximity effect in few-layer graphene sheets
A. Shailos, P. Delplace, A. Kasumov, W. Nativel, C. Collet, R. Deblock, M. Ferrier, S. Guéron, H. Bouchiat
Laboratoire de Physique des Solides, Université Paris-Sud, 91405, Orsay
The physics of the superconducting proximity effect is known to be sensitive to quantum interference in the vicinity of
superconducting/normal (SN) interfaces. In graphene, it has been suggested theoretically that the Andreev reflection of an
electron into a hole at the NS interface, which usually is a retro-reflection, can be specular with a high probability in undoped
samples where the Fermi energy lies in the vicinity of the Dirac point. This is predicted to lead to an unusual bias dependence
of the differential conductance of an SN interface as well as multiple Andreev reflections in S/Graphene/S junctions.
We have found evidence of a superconducting proximity effect in an undoped few-layer-graphene foil connected to
superconducting tungsten electrodes: The resistance decreases by a factor two at low temperature. In addition, the low
temperature differential resistance presents peaks at sub-multiple values of double the superconducting gap of the tungsten
electrodes, a signature of incoherent multiple Andreev reflections in the S/Graphene/S junction. We will discuss the
temperature and field dependence of these peaks, which can be followed up to high field (5 Tesla), thanks to the specificity
of the tungsten electrodes, which is produced by Focused ion beam assisted deposition.
At higher temperature, we find a linearly increasing conductance as a function of bias voltage, which is related to the
linear dispersion relation of graphene [1].
We will also present measurements on a suspended sample whose conductance shows signatures of the phonon modes.
This few-layer graphene sample has also been characterized by high resolution transmission electronic microscopy, enabling
an exact determination of the number of layers.
[1] submitted to Nanoletters, cond-mat 0612058
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Electronic properties of bilayer graphene
V. Fal’ko
University of Lancaster
Résumé
Quasiparticle scattering and local density of states in graphene
Cristina Bena(1), Steven A. Kivelson(2),
(1) SPHT/CEA Saclay,
(2) Stanford University
We determine the effect of quasiparticle interference on the spatial variations of the local density of states (LDOS) in
graphene in the neighborhood of an isolated impurity. We use a T-matrix approach to obtain the quasiparticle interference
spectra for various energies, in the presence of a single impurity. Our predictions can be easily tested experimentally, as very
clean graphene samples are relatively easy to obtain. The resulting Fourier transforms of the scanning tunnelign spectroscopy
(FT-STS) maps can be quite complex, and contain regions of high intensity. Depending on the energy, these regions can be
circular, triangular, or hexagonal. For example, at low energy, the dominant features in the FT-STS maps are circles centered
about the corners and the center of the Brillouin zone. The contours evolve with increasing energy: their radii increase, the
circles centered about the corners become triangular, while the circle in the center becomes a hexagon. Beyond the critical
energy defined by the Van Hove singularity, the topology of the contours changes, and the LDOS exhibits hexagonally
shaped lines of high intensity centered about the center of the BZ. With increasing energy these lines become smaller and
circular again, and they disappear altogether at even higher energies. A comparison between our results and scanning
tunneling microscopy experiments could provide a critical test of the range (of energy) of applicability of the Fermi liquid
description of graphene, where some evidence of the breakdown of Fermi liquid theory has recently been discussed.
Effect of the spin-orbit coupling on the photocurrent in graphene
R-J. Tarento et P. Joyes,
Laboratoire de Physique des Solides, Université Paris-Sud, 91405, Orsay
One-photon and two-photon electronic excitations are investigated for graphene including the spin-orbit coupling (SOC) for
the low energy states. We study in particular the effect of the SOC on the asymmetry in the momentum space distribution of
the excited carriers versus the relative polarizations and phases of the incident fields.
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Dirac and Normal Fermions in Graphite and Graphene: Implications to the Quantum Hall
Igor Luk’yanchuk
Laboratoire de Physique de la Matière Condensée, Université de Picardie Jules Verne
Spectral analysis of Shubnikov de Haas (SdH) oscillations of magnetoresistance and of Quantum Hall Effect (QHE)
measured in quasi-2D highly oriented pyrolytic graphite (HOPG) [1] reveals two types of carriers: normal (massive)
electrons with Berry phase 0 and Dirac-like (massless) holes with Berry phase pi. [2]. We demonstrate [3] that recently
reported integer- and semi-integer QHE for bi-layer and single-layer graphenes take place simultaneously in HOPG samples.
[1] Y. Kopelevich et al.
Phys. Rev. Lett. 90, 156402 (2003)
[2] I. Lukyanchuk, Y. Kopelevich Phys. Rev. Lett. 93, 166402 (2004)
[3] I. Lukyanchuk, Y. Kopelevich Phys. Rev. Lett. 97, 256801 (2006)
Magneto-transmission spectroscopy of graphene
G. Martinez, M.L. Sadowski, M. Potemski, C.Berger, W. deHeer, Y. Bychkov
GHMFL-CNRS 25, Avenue des Martyrs, 38042 Grenoble
Graphene is a monolayer of graphite with a band structure composed of two cones located at two inequivalent corners K and
K’ of the Brillouin zone at which conduction and valence bands merge. In contrast to conventional two dimensional electron
gases, the dispersion relation obeys a Dirac law with an energy linear as a function of momentum which leads to a specific
square root dependence of the Landau levels under an applied magnetic field. The optical response of Graphene reveals
therefore signatures which are specific of the “relativistic” character of the band structure not only in the nature of the
transitions which are observed but also in their energy variation and oscillator strength of the transitions as a function of the
magnetic field. A brief review of these properties will be given. It is found indeed, as expected, that all properties depend on
a single parameter, the Fermi velocity. However the value of this parameter is dependent on the optical properties which are
studied.
To explain, at least in part, this peculiar behavior, the effect of electron-electron interactions, between these Dirac-type
particles, has been evaluated in the Hartree-Fock approximation, including the RPA approximation: these effects are shown
to lead to a re-normalization of the Fermi velocity which depends on the observed optical transition. These predictions will
be compared to the present available experimental results.
Electron interactions in graphene in a strong magnetic field
M. Goerbig, R. Moessner and B. Doucot
Theoreticl Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, England
Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees
of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2)
symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto
the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation;
in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter
in different guises. We discuss consequences for the fractional quantum Hall Effect and the Skyrmionic quasiparticles
[Phys. Rev. B 74, 161407 (2006)].
Effet Hall quantique fractionnaire dans le graphène
N. Regnault et M.O. Goerbig
[1] Laboratoire de Physique des Solides, Université Paris-Sud, 91405, Orsay
[2] Laboratoire Pierre Aigrain, Département de Physique de l'ENS, 75005 Paris.
Alors que l'effet Hall quantique entier fut observé peu de temps après l'obtention des premiers échantillons de graphène, la
mesure l'effet Hall quantique fractionnaire (EHQF) dans le graphène résiste encore aux expérimentateurs. Comme dans le cas
des gaz bidimensionnels d'électrons dans les hétérostructures semiconductrices, l'EHQF est intimement lié aux interactions
entre les électrons et à la dégénérescence des niveaux de Landau. Le caractère relativiste des porteurs de charge ne joue pas a
priori un rôle fondamental ici. D'un point de vue théorique, l'EHQF dans ces nouveaux systèmes semble donc être sans
surprise.
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Mais l'existence d'un degré de liberté interne SU(4) provenant du spin et de la dégénérescence de vallée des électrons, laisse
entrevoir une physique au-delà de celle des gaz bidimensionnels usuels d'électrons. Nous dresserons la liste des différentes
approches théoriques qui ont été proposées dans la littérature pour en tenir compte. Le rôle de la symétrie SU(4) sera détaillé
dans le cas de la généralisation des fonctions d'onde de Halperin[1] pour inclure ce degré de liberté interne.
[1] arXiv:cond-mat/0701661v1
Influence de la courbure de plans de graphène sur les propriétés d’adsorption
F. Valsaque1, H. Le1, M. Arab2, F. Picaud2, Ch. Ramseyer2, E. McRae1
1
2
LCSM, UMR CNRS 7555, Université H. Poincaré, BP 239, 54506 Vandœuvre-les-Nancy, France
LPM, UMR CNRS 6624, Université de Franche-Comté, 16 rte de Gray, 25030 Besançon, France
La physisorption de gaz tels que Kr, Xe ou CH4 sur des surfaces uniformes, c'est-à-dire constituées d’un seul type de plan
cristallin sans défauts, correspond à la formation de couches monomoléculaires successives de l’adsorbat (gaz) sur
l’adsorbant (surface). Ce type d’adsorption, qui donne lieu à des isothermes à marches représentatives de transitions
bidimensionnelles, a été largement étudié sur le graphite qui constitue un substrat uniforme de référence. De par leur filiation
avec ce substrat, il est possible d’étendre ces études aux nanotubes de carbone qui sont constitués d’une ou de plusieurs
feuilles de graphène (nanotubes mono- ou multi-parois) enroulées en cylindres sans raccord.
L’adsorption sur les nanotubes monoparois donne également lieu à des isothermes à marches, permettant de mettre en
évidence des fractions de surfaces uniformes et d’obtenir des informations sur la nature des sites d’adsorption [1-2]. La
comparaison des isothermes avec celles obtenues sur le graphite conduit à préciser l’influence de la morphologie des
faisceaux de tubes sur les propriétés d’adsorption. En particulier le rôle de la courbure des plans de graphène sur la valeur des
énergies d’adsorption est mis en évidence à partir d’échantillons de nanotubes ayant différents diamètres caractéristiques. Ces
résultats expérimentaux sont confirmés par ceux de simulations qui montrent notamment que plus le diamètre des tubes est
grand plus l’énergie d’adsorption est proche de celle d’un plan de graphène idéal [3].
[1] E. McRae, M.-R. Babaa, F. Valsaque and K. Masenelli-Varlot, Gas adsorption on carbon nanotubes, Rec. Dev. Surf. Sci., Transworld
Res. Net., 1 (2004) 51.
[2] M. Arab, F. Picaud, Ch. Ramseyer, R. Babaa, F. Valsaque, E. McRae, Chem. Phys. Lett, 423 (2006) 183.
[3] M. Arab, F. Picaud, Ch. Ramseyer, R. Babaa, F. Valsaque, E. McRae, J. Chem. Phys. 126 1/10 (2007) 54709.
Spatially resolved Raman spectroscopy of Single- and Few-Layer Graphene
D. Graf, Françoise Molitor, Klaus Ensslin, Christoph Stampfer, Alain Jungen, and Christopher Hierold
ETH Zurich, Switzerland
L. Wirtz
Institute for Electronics, Microelectronics, and Nanotechnology, Lille
Using a scanning confocal approach, we show that Raman spectroscopy can spatially resolve the number of layers in flakes
of single- and few-layer graphene deposited on a SiO2 substrate. The most prominent difference between the spectra of the
single and the double-layer is the width of the D* line which splits into different sub-peaks. For the interpretation of the
differences in the spectra, the double-resonant Raman model [1] which involves electron-hole pair excitations is qualitatively
successful [2]. Quantitative evaluation based on DFT band-structures and phonon dispersions display, however, a mismatch
between theory and experiments [3]. We discuss the achievements and short-comings of the double-resonant model for the
explanation of the differences in the Raman spectra of single-layer, few-layer, and bulk graphite and its consequences for the
interpretation of nanotube Raman spectra.
[1] C. Thomsen and S. Reich, Phys. Rev. Lett. 85, 5214 (2000).
[2] A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K.
Geim, Phys. Rev. Lett. 97, 187401 (2006).
[3] D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, Nano Lett. 7, 238 (2007).
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Realization of Massless Dirac Fermions with Cold Atoms
B. Grémaud1, Ch. Miniatura2,3 et B.-G. Englert3
1 Institut
Non-Linéaire de Nice, 1361, route des Lucioles, F-06560 Valbonne
Kastler-Brossel, UPMC, 4, place Jussieu, F-75252 Paris Cedex 5
3Department of Physics,National Univerity of Singapore, 2 Science Drive 3
Singapore 117542
2 Laboratoire
In 2004, researchers in Manchester isolated one-atom thick sheets of carbon atoms, the atoms being organized in a planar
honeycomb structure [1]. Such a material, a single layer of graphite, is referred to as "graphene" and is of uttermost
importance in condensed matter physics since by wrapping it one gets carbon nanotubes or fullerenes. For theorists, such a
system is also of great interest because it provides a physical realization of two dimensional field theories with sign
anomalies [2]. Indeed, it can be easily shown that the continuum limit of the effective theory describing the electronic
transport in graphene is that of two-dimensional massless Dirac fermions. Since then, an intense activity has flourished in the
field [3,4].
It is now well established that some condensed-matter phenomena can be easily reproduced by loading ultra-cold atoms in
optical lattices, a system that under many circumstances has proven quite flexible [5,6]. The great advantage is that the
relevant parameters are easily and accurately controlled (shape and strength of the light potential, atom-atom interactions,
etc) while spurious effects destroying the quantum coherence (for example, the analog of the electron-phonon interaction is
completely absent) can be easily circumvented. In particular, by superposing 3 coplanar lasers beams (linearly polarized
orthogonal to the plane) propagating along directions with consecutive angles of 60 degrees, one precisely realizes an optical
potential where the minima are organized in a honeycomb structure, reproducing the unique situation found in graphene. We
will discuss the specific properties of cold atomic fermions in such a situation: band structure, effective Hamiltonian, Dirac
field, dependence of the “Fermi velocity” on the experimental parameters, etc. In addition, we will discuss the possibilities of
realizing the analog of the Fractional Quantum Hall Effect [7,8] by inducing an effective magnetic field in the system.
[1] K.S. Novoselov et al., Science 306, 666 (2004).
[2] G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984).
[3] Physics Today, January 2006, page 21.
[4] Physics Worls, November 2006, page 1.
[5] G. Grynberg and C. Robilliard, Phys. Rep. 355, 335 (2001).
[6] V. Ahufinger V et al., Phys. Rev. A 72, 063616 (2005).
[7] K.S. Novoselov et al., Nature 438, 197 (2005).
[8] Y.B. Zhang et al., Nature 438, 201 (2005).
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