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Etude de l'effet Hall quantique dans le graphène exfolié en vue d'une application en métrologie quantique

Abstract : The quantum Hall effect (QHE) observed in two dimensional electron gases (2DEGs) at low temperature and under high magnetic induction, has revolutionized the resistance metrology because it leads to a universal and very reproducible quantum resistance standard only dependent on e and h (respectively the electron charge and Planck's constant). One of the metrologists' missions is to develop standards with improved performances and to notably make them more practical, working for example at higher temperature or lower magnetic induction. In this context, graphene physics could be very interesting for metrological applications. Monolayer graphene is a one atom thick layer of carbon atoms condensed in a honeycomb lattice. A bilayer graphene consists in two stacked monolayers. Larger energy spacings between the first Landau Levels in monolayer and in bilayer than in GaAs make the QHE in graphene more robust and give hope that more practical standards could be developed. During the PhD, we have set a protocol up in order to fabricate exfoliated graphene based Hall bars, including location with an optical microscope, e-beam lithography, metallization, plasma etching… Backgated using oxidized silicon wafers the devices were designed to fulfill at best the metrological requirements (large conduction channel, well defined voltage probes…). At low temperature, the typical charge carrier residual doping obtained after the annealing process was 3-4x1011 cm-2. Mobilities were close to 3000 cm2/(V.s) and 4000 cm2/(V.s) respectively for the monolayer and the bilayer based device both for holes and electrons. Mesoscopic transport was characterized at low temperature by weak localization and universal conductance fluctuations (UCF) measurements. The phase coherence length deduced was about 0.5 µm below 1.5 K. The resistance of the contacts, measured in the QHE regime, appeared to be rather low (typically few ohms). The QHE was investigated in details at low temperature (300 mK < T <1.5 K) and high magnetic field (up to 18.5 T) in both monolayer and bilayer graphene by refined measurements of the Hall resistance (RH) and also of the longitudinal resistance (Rxx). The accurate measurements of RH were performed using a Cryogenic Current Comparator based resistance bridge. They consist in an indirect comparison between the QHE in graphene and the QHE obtained in a GaAs based Hall bar, supposed to deliver the expected value RH/2. Our measurements showed an agreement of the Hall resistance in graphene with the expected value within some parts in 107. At the lowest biasing current and in the lowest dissipation state (where Rxx→0) it is possible to demonstrate an agreement within an uncertainty of 3 parts in 107. That accuracy is essentially limited by the small size, and the poor homogeneity of the carrier density of the graphene electronic systems, both acting for a very reduced breakdown current of the QHE (1-2 µA). Nevertheless these results are the most accurate tests of the QHE performed in exfoliated graphene and the first universality test of the QHE with bilayer graphene. They confirm the potential of the QHE in graphene for the metrological application.
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Jérémie Guignard. Etude de l'effet Hall quantique dans le graphène exfolié en vue d'une application en métrologie quantique. Autre [cond-mat.other]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112116⟩. ⟨tel-00664374⟩

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