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Since the very first investigations of the electronic properties of graphene the nature of the scattering disorder potential has been shown to play an essential role in determining the carrier density dependence of the conductance. Impurity scattering is characterized by two different times the transport and elastic scattering times which are sensitive to the linear energy dispersion of graphene. The analysis of the ratio between these two times gives insight on the nature (neutral or charged) and range of the scatterers. We discuss how to extract these two times from magneto-transport measurements and analyze their differences in monolayer and bilayer Graphene in relation with the different symmetry properties of their band structure and wave functions. We show that whereas short range impurity scattering is the dominant mechanism limiting the classical transport, phase coherent mesoscopic transport is very sensitive to long range disorder. In particular, the formation of electron/hole puddles in the vicinity of the charge neutrality point strongly affects the amplitude of the conductance fluctuations and the induced supercurrent in the presence of superconducting electrodes. [ABSTRACT FROM AUTHOR]

The high tunability of the density of states of graphene makes it an ideal probe of quantum transport in different regimes. In particular, the supercurrent that can flow through a nonsuperconducting (N) material connected to two superconducting (S) electrodes, crucially depends on the length of the N relative to the superconducting coherence length. Using graphene as the N material we have investigated the full range of the superconducting proximity effect, from short to long diffusive junctions. By combining several S/graphene/S samples with different contacts and lengths, and measuring their gate-dependent critical currents (Ic) and normal state resistance RN, we compare the product eRNIc to the relevant energies, the Thouless energy in long junctions and the superconducting gap of the contacts in short junctions, over three orders of magnitude of Thouless energy. The experimental variations strikingly follow a universal law, close to the predictions of the proximity effect both in the long and short junction regime, as well as in the crossover region, thereby revealing the interplay of the different energy scales. Differences in the numerical coefficients reveal the crucial role played by the interfacial barrier between graphene and the superconducting electrodes, which reduces the supercurrent in both short and long junctions. Surprisingly, the reduction of supercurrent is independent of the gate voltage and of the nature of the electrodes. A reduced induced gap and Thouless energy are extracted, revealing the role played by the dwell time in the barrier in the short junction, and an effective increased diffusion time in the long junction. We compare our results to the theoretical predictions of Usadel equations and numerical simulations, which better reproduce experiments with imperfect NS interfaces. [ABSTRACT FROM AUTHOR]

Inducing magnetism in graphene holds great promises, such as controlling the exchange interaction with a gate electrode, and generating exotic magnetic phases. Coating graphene with magnetic molecules or atoms has so far mostly led to decreased graphene mobility. In the present work, we show that Pt-porphyrin molecules adsorbed on graphene lead both to an enhanced mobility, and to gate-dependent magnetism. We report that porphyrins can act both as donor or acceptor molecules, depending on the initial doping of the graphene sheet. The porphyrins transfer charge and ionize around the charged impurities on graphene, and, consequently, the graphene doping is decreased and its mobility is enhanced. In addition, ionized porphyrin molecules carry a magnetic moment. Using the sensitivity of mesoscopic transport to magnetism, in particular, the superconducting proximity effect and conductance fluctuations, we explore the magnetic order induced in graphene by the interacting magnetic moments of the ionized porphyrin molecules. Among the signatures of magnetism, we find two-terminal-magnetoresistance fluctuations with an odd component, a tell-tale sign of time-reversal symmetry breaking at zero field, which does not exist in uncoated graphene samples. When graphene is connected to superconducting electrodes, the induced magnetism leads to a gate-voltage-dependent suppression of the supercurrent, modified magnetic interference patterns, and gate-voltage-dependent magnetic hysteresis. The magnetic signatures are greatest for long superconductor/graphene/superconductor junctions, and for samples with the highest initial doping, compatible with a greater number of ionized, and thus magnetic porphyrin molecules. Our findings suggest that long-range (of the order of the coherence length, or micrometers) magnetism is induced through graphene by the ionized porphyrins' magnetic moment. This magnetic interaction is controled by the density of carriers in graphene, a tunability that could be exploited in spintronic applications. [ABSTRACT FROM AUTHOR]

We investigate the superconducting proximity effect through graphene in the long diffusive junction limit, at low and high magnetic field. The interface quality and sample phase coherence lead to a zero-resistance state at low temperature, zero magnetic field, and high doping. We find a striking suppression of the critical current near graphene's charge neutrality point, which we attribute to specular reflection of Andreev pairs at the interface of charge puddles. This type of reflection, specific to the Dirac band structure, had up to now remained elusive. At high magnetic field, the use of superconducting electrodes with high critical field enables the investigation of the proximity effect in the quantum Hall regime. Although the supercurrent is not directly detectable in our two-wire configuration, interference effects are visible which may be attributed to the injection of Cooper pairs into edge states. [ABSTRACT FROM AUTHOR]

We demonstrate the enhanced robustness of the supercurrent through graphene-based Josephson junctions in which strong spin-orbit interactions (SOIs) are induced. We compare the persistence of a supercurrent at high out-of-plane magnetic fields between Josephson junctions with graphene on hexagonal boron-nitride and graphene on WS2, where strong SOIs are induced via the proximity effect. We find that in the shortest junctions both systems display signatures of induced superconductivity, characterized by a suppressed differential resistance at a low current, in magnetic fields up to 1 T. In longer junctions, however, only graphene on WS2 exhibits induced superconductivity features in such high magnetic fields, and they even persist up to 7 T. We argue that these robust superconducting signatures arise from quasiballistic edge states stabilized by the strong SOIs induced in graphene by WS2. [ABSTRACT FROM AUTHOR]

We demonstrate strong anisotropic spin-orbit interaction (SOI) in graphene induced by monolayer WS2. Direct comparison between graphene-monolayer WS2 and graphene-bulk WS2 systems in magnetotransport measurements reveals that monolayer transition metal dichalcogenide can induce much stronger SOI than bulk. Detailed theoretical analysis of the weak antilocalization curves gives an estimated spin-orbit energy (Eso) higher than 10 meV. The symmetry of the induced SOI is also discussed, and the dominant z→-z symmetric SOI can only explain the experimental results. Spin relaxation by the Elliot-Yafet mechanism and anomalous resistance increase with temperature close to the Dirac point indicates Kane-Mele SOI induced in graphene. [ABSTRACT FROM AUTHOR]