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The pairing of electrons is ubiquitous in electronic systems featuring attractive inter-electron interactions, as exemplified in superconductors. Counterintuitively, it can also be mediated in certain circumstances by the repulsive Coulomb interaction alone. Quantum Hall (QH) Fabry-Pérot interferometers (FPIs) tailored in a two-dimensional electron gas under a perpendicular magnetic field have been argued to exhibit such an unusual electron pairing, seemingly without attractive interactions. Here, we show evidence in graphene QH FPIs, revealing not only a similar electron pairing at bulk filling factor ν B  = 2, but also an unforeseen emergence of electron tripling characterized by a fractional Aharonov-Bohm flux period of h/3e (h is the Planck constant and e the electron charge) at ν B  = 3. Leveraging plunger-gate spectroscopy, we demonstrate that electron pairing (tripling) involves correlated charge transport on two (three) entangled QH edge channels. This spectroscopy indicates a quantum interference flux periodicity determined by the sum of the phases acquired by the distinct QH edge channels having slightly different interfering areas. Phase jumps observed in the pajama maps can be accounted for by the frequency beating between pairing/tripling modes and the outer interfering edge., Competing Interests: Competing interests: The authors declare no competing interests., (© 2024. The Author(s).)

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states, e.g. , snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers., (Creative Commons Attribution license.)

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation 1-3 . However, despite recent experimental progress towards this hybridization 4-15 , concrete evidence for a chiral QH Josephson junction 16 -the elemental building block for coherent superconducting QH circuits-is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ 0 magnetic flux periodicity 16-19 (ϕ 0  = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e 2  ≈ 12.9 kΩ. We observe reproducible 2ϕ 0 -periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface 19-22 . Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes 23-32 ., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

2D materials offer the ability to expose their electronic structure to manipulations by a proximity effect. This could be harnessed to craft properties of 2D interfaces and van der Waals heterostructures in devices and quantum materials. We explore the possibility to create an artificial spin polarized electrode from graphene through proximity interaction with a ferromagnetic insulator to be used in a magnetic tunnel junction (MTJ). Ferromagnetic insulator/graphene artificial electrodes were fabricated and integrated in MTJs based on spin analyzers. Evidence of the emergence of spin polarization in proximitized graphene layers was observed through the occurrence of tunnel magnetoresistance. We deduced a spin dependent splitting of graphene's Dirac band structure (∼15 meV) induced by the proximity effect, potentially leading to full spin polarization and opening the way to gating. The extracted spin signals illustrate the potential of 2D quantum materials based on proximity effects to craft spintronics functionalities, from vertical MTJs memory cells to logic circuits.