A novel promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect [1,2] . Despite this potential, signatures of superconductivity in the quantum Hall regime remain scarce [5][6][7][8][9][10][11] , and a superconducting current through a QH weak link has so far eluded experimental observation. Here we demonstrate the existence of a new type of supercurrent-carrying states in a QH region at magnetic fields as high as 2 Tesla. The observation of supercurrent in the quantum Hall regime marks an important step in the quest for exotic topological excitations such as Majorana fermions and parafermions, which may find applications in fault-tolerant quantum computations.1 arXiv:1512.09083v1 [cond-mat.mes-hall] Dec 2015The interplay of the quantum Hall effect with superconductivity is expected to result in novel excitations with non-trivial braiding statistics such as Majorana fermions and non-abelian Majorana anyons [1][2][3][4] . When a quantum Hall region is contacted by two superconducting electrodes, the gapped QH bulk prevents the flow of a supercurrent. However, it was predicted more than 20 years ago that the supercurrent may still be mediated by QH edge states [12] . Due to its chiral nature, a single edge can only conduct charge carriers in one direction, so both edges have to be involved in establishing supercurrent between the two contacts. This situation is fundamentally different from the Josephson junctions made of two-dimensional topological insulators, where each edge can support its own supercurrent [13][14][15][16] . Indeed, contrary to the case of topological insulators, the magnetic field in the QH regime breaks time-reversal symmetry, which is essential for the s-wave pairing of conventional superconductors. Nonetheless, we observe a robust supercurrent in the quantum Hall regime, which we attribute to an unconventional form of Andreev bound states circulating along the perimeter of the QH region and involving electron and hole trajectories separated by several micrometers. We performed transport measurements on four Josephson junctions (J 1−4 ) made of graphene encapsulated in boron nitride and contacted by electrodes made of a molybdenum-rhenium alloy [Fig. 1a] [11] , a type II superconductor with a high upper critical field of H c2 =8 T. The high quality of these heterostructures allowed us to observe Fabry-Perot oscillations of the junctions' resistance and critical current, indicating that the transmission of charge carriers between the contacts is ballistic [17] . The supercurrent is uniformly distributed along the width of the contacts, as evidenced by the regular Fraunhofer pattern [18] measured at small magnetic fields [17] . All junctions demonstrate supercurrent in the QH regime; for consistency, we choose to present data measured on sample J 1 , which has a distance between contacts L = 0.3 µm and a width of the contacts W = 2.4µm (see Figure 1b). Recent preprint reported on the observation of supercurrent ...

We investigate the critical current, I C , of ballistic Josephson junctions made of encapsulated graphene/boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, I C is found to scale as ∝ exp(−k B T /δE). The extracted energies δE are independent of the carrier density and proportional to the level spacing of the ballistic cavity, as determined from Fabry-Perot oscillations of the junction normal resistance. As T → 0 the critical current of a long (or short) junction saturates at al level determined by the product of δE (or ∆) and the number of the junction's transversal modes.1 arXiv:1604.07320v3 [cond-mat.mes-hall] Oct 2016Encapsulated graphene/boron-nitride heterostructures emerged in the past year as a medium of choice for studying proximity-induced superconductivity in the ultra-clean limit [1][2][3][4]. These junctions support the ballistic propagation of superconducting currents across micron-scale graphene channels, and their critical current is gate-tunable across several orders of magnitude. In these devices, a rich phenomenology arises from the interplay of superconductivity with ballistic transport [1], cyclotron motion [2], and even the quantum Hall effect at high magnetic field [4]. In a superconductor -normal metal -superconductor (SNS) junction, single particles in the N region cannot enter the superconductor and therefore experience Andreev reflections at each S-N interface. This results in Andreev bound states (ABS), which are capable of 2 carrying superconducting current across the N region. In long ballistic junctions, the energy spectrum of the ABS is quantized with a level spacing of T is independent of V G . In the case of long ballistic graphene junctions, the inverse slope δE is expected to be independent of the carrier density and inversely proportional to L.In this work we study several ballistic junctions of different length and demonstrate that the temperature dependence of the critical current dramatically differs in the long and short regimes. For long junctions, we observe an exponential scaling of the current through the [5, 6,10,11]. Note that in graphene v F is a constant, and δE is expected to be independent of the carrier density or the mobility , 17-21], which could be attributed to either underdamped junction dynamics [8,20], or to the self-heating by the retrapping current [1,23]. As discussed in the supplementary material, the second scenario is more likely for most of the range studied here. Based on the measurements of the switching statistics [16,[24][25][26], in the following we will use the switching current to represent the true critical current of the junction, I C .In the hole-doped regime, the reflections of ballistic charge carriers from the n-doped contact interfaces yield the quantum ("Fabry-Perot") interference. A very similar oscillation pattern could be observed in the dependence of both the the normal conductance, G N , and the critica...

The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields.

The fate of the low-temperature conductance at the charge-neutrality (Dirac) point in a single sheet of graphene on boron nitride is investigated down to 20 mK. As the temperature is lowered, the peak resistivity diverges with a power-law behavior and becomes as high as several megohms per square at the lowest temperature, in contrast with the commonly observed saturation of the conductivity. As a perpendicular magnetic field is applied, our device remains insulating and directly transitions to the broken-valley-symmetry, ν=0 quantum Hall state, indicating that the insulating behavior we observe at zero magnetic field is a result of broken valley symmetry. Finally we discuss the possible origins of this effect.