Electron wave and quantum optics in graphene

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

Electron quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in many 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

Effet de proximité entre un supraconducteur à haute température critique et du graphène

We have fabricated YBCO graphene junction. We studied the electronical transport at the interface between these two materials as well as the mechanism - the Andreev reflexion- by which a current carried by electrons is transformed into a current carried by Cooper pairs. We observed electronic interferences as a function of graphene doping. This modulation comes from the presence of a potential barrier at the interface between YBCO and graphene in which the particles are circulating before being transmitted or reflected. These interferences correspond to Klein tunneling of normal electrons when their energy is higher than the superconducting gap. At lower energy, Cooper pairs can traverse the barrier by Klein tunneling. We later fabricated YBCO graphene junctions which size is comparable to the graphene coherence length. We observed tunnel conductance when the interface between graphene and YBCO is opaque. In the case when the interface is transparent, we observed oscillations of the junction conductance as a function of the bias voltage and of the gate voltage. These oscillations seem to originate from electronic interferences inside the graphene channel between the superconducting electrodes. We also propose an experimental method to fabricate phi junction based on BSCCO.Nous avons fabriqué des jonctions YBCO graphène, nous avons étudié dans un premier temps le transport électronique à l'interface entre ces deux matériaux ainsi que le mécanisme - la réflexion d'Andreev - par lequel un courant porté par des électrons est transformé en courant par des paires de Cooper. Nous avons observé des interférences électroniques en fonction du niveau de dopage du graphène. Ces interférences correspondent au tunneling de Klein d'électrons normaux quand l'énergie de ces électrons dépassent le gap supraconducteur. A plus basse énergie, ce sont les paires de Cooper qui passent la barrière par effet tunnel de Klein. Dans un deuxième temps, nous avons fabriqué des jonctions YBCO graphène dont la taille est comparable à la longueur de cohérence du graphène. Nous avons observé d'une part un comportement tunnel de la conductance dans le cas où l'interface graphène YBCO est sale. Dans le cas où l'interface YBCO graphène est propre, nous avons observé des oscillations de la conductance de la jonction en fonction de la tension de biais ainsi que de la tension de grille. Ces oscillations semblent provenir d'interférences électroniques dans le canal de graphène entre les électrodes supraconductrices. Enfin, nous présentons une nouvelle méthode de fabrication de jonction phi à base de BSCCO

Evidence for chiral supercurrent in quantum Hall Josephson junctions

Maintext and SIHybridizing superconductivity with the quantum Hall (QH) effects has major potential for designing novel circuits capable of inducing and manipulating non-Abelian states for topological quantum computation. However, despite recent experimental progress towards this hybridization, concrete evidence for a chiral QH Josephson junction -- 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 $2\phi_0$ magnetic flux periodicity ($\phi_0=h/2e$ is the superconducting flux quantum, $h$ the Planck constant and $e$ the electron charge). Here, we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit such a chiral supercurrent, visible up to 8 teslas, and carried by the spin-degenerate edge channel of the QH plateau of resistance $h/2e^2\simeq 12.9$ k$\Omega$. We observe reproducible $2\phi_0$-periodic oscillation of the supercurrent, which emerges at 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 pivotal to obtain a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface. Our findings mark a critical milestone along the path to explore correlated and fractional QH-based superconducting devices that should host non-Abelian Majorana and parafermion zero modes

Electron wave and quantum optics in graphene

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

Evidence for correlated electron pairs and triplets in quantum Hall interferometers

Pairing of electrons is ubiquitous in electronic systems featuring attractive inter-electron interactions, as exemplified in superconductors. Counter-intuitively, it can also be mediated in certain circumstances by the repulsive Coulomb interaction alone. Quantum Hall (QH) Fabry-Pérot interferometers (FPIs) tailored in two-dimensional electron gas under a perpendicular magnetic field has been argued to exhibit such unusual electron pairing seemingly without attractive interaction. Here, we show evidence in graphene QH FPIs revealing not only a similar electron pairing at bulk filling factor nu=2 but also an unforeseen emergence of electron tripling characterized by a fractional Aharonov-Bohm flux period h/3e (h is the Planck constant and e the electron charge) at nu=3. Leveraging a novel 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. While recent theory invokes the dynamical exchange of neutral magnetoplasmons -- dubbed neutralons -- as mediator for electron pairing, our discovery of three entangled QH edge channels with apparent electron tripling defies understanding and introduces a new three-body problem for interacting fermions

Data for Evidence for chiral supercurrent in quantum Hall Josephson junctions

Data for the figures of the article entitled "Evidence for chiral supercurrent in quantum Hall Josephson junctions"