Fractional Quantum Hall Effect in Suspended Graphene: Transport Coefficients and Electron Interaction Strength

Strongly correlated electron liquids which occur in quantizing magnetic fields reveal a cornucopia of fascinating quantum phenomena such as fractionally charged quasiparticles, anyonic statistics, topological order, and many others. Probing these effects in GaAs-based systems, where electron interactions are relatively weak, requires sub-kelvin temperatures and record-high electron mobilities, rendering some of the most interesting states too fragile and difficult to access. This prompted a quest for new high-mobility systems with stronger electron interactions. Recently, fractional-quantized Hall effect was observed in suspended graphene (SG), a free-standing monolayer of carbon, where it was found to persist up to T=10 K. The best results in those experiments were obtained on micron-size flakes, on which only two-terminal transport measurements could be performed. Here we pose and solve the problem of extracting transport coefficients of a fractional quantum Hall state from the two-terminal conductance. We develop a method, based on the conformal invariance of two-dimensional magnetotransport, and illustrate its use by analyzing the measurements on SG. From the temperature dependence of longitudinal conductivity, extracted from the measured two-terminal conductance, we estimate the energy gap of quasiparticle excitations in the fractional-quantized nu=1/3 state. The gap is found to be significantly larger than in GaAs-based structures, signaling much stronger electron interactions in suspended graphene. Our approach provides a new tool for the studies of quantum transport in suspended graphene and other nanoscale systems

Critical currents in graphene Josephson junctions

We study the superconducting correlations induced in graphene when it is placed between two superconductors, focusing in particular on the supercurrents supported by the 2D system. For this purpose we make use of a formalism placing the emphasis on the many-body aspects of the problem, with the aim of investigating the dependence of the critical currents on relevant variables like the distance L between the superconducting contacts, the temperature, and the doping level. Thus we show that, despite the vanishing density of states at the Fermi level in undoped graphene, supercurrents may exist at zero temperature with a natural 1/L^3 dependence at large L. When temperature effects are taken into account, the supercurrents are further suppressed beyond the thermal length L_T (~ v_F / k_B T, in terms of the Fermi velocity v_F of graphene), entering a regime where the decay is given by a 1/L^5 dependence. On the other hand, the supercurrents can be enhanced upon doping, as the Fermi level is shifted by a chemical potential \mu from the charge neutrality point. This introduces a new crossover length L* ~ v_F / \mu, at which the effects of the finite charge density start being felt, marking the transition from the short-distance 1/L^3 behavior to a softer 1/L^2 decay of the supercurrents at large L. It turns out that the decay of the critical currents is given in general by a power-law behavior, which can be seen as a consequence of the perfect scaling of the Dirac theory applied to the low-energy description of graphene.Comment: 11 pages, 6 figures, to appear in J. Phys.: Condens. Matte

Integer and Fractional Quantum Hall Effect in Two-Terminal Measurements on Suspended Graphene

We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic samples. New quantized states are found at integer Landau level fillings outside the sequence 2,6,10.., as well as at a fractional filling \nu=1/3. Their presence is revealed by plateaus in the two-terminal conductance which appear in magnetic fields as low as 2 Tesla at low temperatures and persist up to 20 Kelvin in 12 Tesla. The excitation gaps, extracted from the data with the help of a theoretical model, are found to be significantly larger than in GaAs based electron systems.Comment: 17 pages, 4 figure

Harmonisation and diagnostics of MIPAS ESA CH4 and N2O profiles using data assimilation

This paper discusses assimilation experiments of methane (CH4) and nitrous oxide (N2O) profiles retrieved from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). Here we focus on data versions 6 and 7 provided by the ESA processor. These data sets have been assimilated by the Belgian Assimilation System for Chemical ObsErvations (BASCOE). The CH4 and N2O retrieved profiles can oscillate, especially in the tropical lower stratosphere. Using the averaging kernels of the observations and a background error covariance matrix, which has previously been calibrated, allows the system to partly remedy this issue and provide assimilated fields that are more regular vertically. In general, there is a good agreement between the BASCOE analyses and independent observations from ACE–FTS (CH4 and N2O) and MLS (N2O), demonstrating the general good quality of CH4 and N2O retrievals provided by MIPAS ESA. Nevertheless, this study also identifies two issues in these data sets. First, time series of the observations show unexpected discontinuities due to an abrupt change in the gain of MIPAS band B, generally occurring after the instrument decontamination. Since the calibration is performed weekly, the abrupt change in the gain affects the measurements until the subsequent calibration is performed. Second, the correlations between BASCOE analyses and independent observations are poor in the lower stratosphere, especially in the tropics, probably due to the presence of outliers in the assimilated data. In this region, we recommend using MIPAS CH4 and N2O retrievals with caution

Dislocations in graphene

We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations. Two types of dislocations are found to be stable: "glide" dislocations consisting of heptagon-pentagon pairs, and "shuffle" dislocations, an octagon with a dangling bond. Unlike the most studied case of carbon nanotubes, Stone Wales defects are unstable in the planar graphene sheet. Similar defects in which one of the pentagon-heptagon pairs is displaced vertically with respect to the other one are found to be dynamically stable. Shuffle dislocations will give rise to local magnetic moments that can provide an alternative route to magnetism in graphene

Correcting surface winds by assimilating High-Frequency Radar surface currents in the German Bight

Surface winds are crucial for accurately modeling the surface circulation in the coastal ocean. In the present work, high-frequency (HF) radar surface currents are assimilated using an ensemble scheme which aims to obtain improved surface winds taking into account ECMWF (European Centre for Medium-Range Weather Forecasts) winds as a first guess and surface current measurements. The objective of this study is to show that wind forcing can be improved using an approach similar to parameter estimation in ensemble data assimilation. Like variational assimilation schemes, the method provides an improved wind field based on surface current measurements. However, the technique does not require an adjoint and it is thus easier to implement. In addition, it does not rely on a linearization of the model dynamics. The method is validated directly by comparing the analyzed wind speed to independent in situ measurements and indirectly by assessing the impact of the corrected winds on model sea surface temperature (SST) relative to satellite SST.European COastal-shelf sea OPerational observing and forecasting system (ECOOP