The field of 'Valleytronics' has recently been attracting growing interest as a promising concept for the next generation electronics, because non-dissipative pure valley currents with no accompanying net charge flow can be manipulated for computational use, akin to pure spin currents 1 . Valley is a quantum number defined in an electronic system whose energy bands contain energetically degenerate but non-equivalent local minima (conduction band) or maxima (valence band) due to a certain crystal structure. Specifically, spatial inversion symmetry broken two-dimensional honeycomb lattice systems exhibiting Berry curvature is a subset of possible systems that enable optical 2-5

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...

A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.

A quantum phase transition is an abrupt change between two distinct ground states of a many-body system, driven by an external parameter. In the vicinity of the quantum critical point (QCP) where the transition occurs, a new phase may emerge that is determined by quantum fluctuations and is very different from either phase. In particular, a conducting system may exhibit non-Fermi-liquid behaviour. Although this scenario is well established theoretically, controllable experimental realizations are rare. Here, we experimentally investigate the nature of the QCP in a simple nanoscale system-a spin-polarized resonant level coupled to dissipative contacts. We fine-tune the system to the QCP, realized exactly on-resonance and when the coupling between the level and the two contacts is symmetric. Several anomalous transport scaling laws are demonstrated, including a striking non-Fermi-liquid scattering rate at the QCP, indicating fractionalization of the resonant level into two Majorana quasiparticles.Q uantum phase transitions (QPTs) are attracting strong interest in diverse fields of physics, ranging from quantum magnets and strongly correlated materials 1 to, more recently, cold atoms 2 , nanostructures 3,4 and particle physics 5 . The foremost remarkable property of QPTs is the possibility to create exotic quantum states of matter at the QCP, such as deviations from the standard Fermi-liquid paradigm for metals. These zero-temperature states then cause anomalous physical properties at finite temperatures 1 . Another intriguing aspect of QPTs is their behaviour under non-equilibrium conditions, such as either a sudden quench driving the system non-adiabatically through the transition 6 , or a strong perturbation provided by a large current density as typically realized in nanoelectronic devices 7 . Despite the ubiquity of QPTs in contemporary theoretical physics, obtaining clear experimental signatures has been challenging.Here, we present a thorough characterization of all facets of a QPT in a fully tunable single-molecule transistor built from a spinpolarized carbon nanotube quantum dot connected to strongly dissipative contacts 8,9 . As the electronic level of the quantum dot crosses the Fermi energy of the leads, in the standard case of good metallic contacts transport occurs through a resonance of finite width and height. In contrast, the presence of dissipation drives the conductance to zero (in the limit of vanishing temperature), unless one tunes the position of the resonant level to the Fermi energy and simultaneously makes the tunnel barriers between the dot and the two leads perfectly equal. In the latter case, the conductance saturates at the unitary limit, e 2 /h (e is the elementary charge and h is the Planck constant), and the resonance width tends to zero, as we recently demonstrated 9 . A quantum critical state is obtained, whose anomalous properties are the subject of the present study.By optimizing the dissipative environment, we find that the quantum critical properties surprisingly behave very cl...