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The defence will be in English.
Abstract: Combining the Josephson effect, i.e. the transfer of Cooper pairs between two superconducting blocks separated by a sufficiently thin barrier, with the quantum Hall effect regime, in which a current flows via one-dimensional channels along the edges of a two-dimensional electron gas, could, under certain conditions, generate a new type of quasiparticle with non-Abelian exchange statistics. Although these two effects were independently observed more than 40 years ago, the identification of a supercurrent mediated by the edge states of the quantum Hall effect, termed chiral supercurrent, has yet to be demonstrated. In this PhD work, we study Josephson junctions whose normal part is made of graphene in the quantum Hall effect regime. The use of graphene nanoribbons for our samples, combined with electrodes made of MoGe, a disordered superconductor with a critical field above 12 T, has enabled us to observe a supercurrent in the ν = 2 quantum Hall plateau up to a magnetic field value of 8 T, a record for this type of device. Under microwave radiation, the supercurrent forms Shapiro steps indicating a 2π-periodic current-phase relation. Ultra-fast I/V curve measurements have made it possible to systematically investigate this supercurrent as a function of gate voltage, magnetic field and applied current bias. In particular, in the gate voltage-magnetic field plane, the switching current value (extracted from successive I/V curves) exhibits oscillations in the region corresponding to the ν = 2 quantum Hall plateau. We also observe oscillations in the differential resistance calculated from these I/V curves. At fixed gate voltage, in our smallest junctions, the magnetic field period of these oscillations cannot be related to the usual value of the superconducting flux quantum h/2e, even considering the uncertainty in the estimated area of our devices. However, at constant filling factor ν, the period corresponds to a flux quantum h/e, a value anticipated by theories dealing with a supercurrent mediated by the quantum Hall edge states. In addition, the application of a Fourier analysis to these oscillations unveils a reduction in their period as the filling factor increases, an observation that gives us an access to the dispersion of Landau levels at the graphene’s edges. Fourier analysis also reveals a reduction in the oscillations’ period as the magnetic field increases, which we explain by the latter’s influence on the spatial extension of the wave functions of the quantum Hall edge channels. Finally, a study of the dependence of the resistance oscillations on the voltage reveals a checkerboard-like pattern, an observation reminiscent of the interference effects signatures usually reported in analogues of Fabry-Perot interferometers in the quantum Hall effect regime. Extending this analogy, it is possible to estimate the Thouless energy associated with the charge carriers involved in these interference effects, and consequently to demonstrate a renormalization of the velocity of the quantum Hall edge states along the graphene-superconductor interfaces.
