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When a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect─the phase of the junction locks to the drive frequency. As a result, the I-V curves of the junction acquire "Shapiro steps" of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multiterminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe robust fractional Shapiro steps and correlated switching events, which can only be explained by considering the device as a completely connected Josephson network. We successfully simulate the observed behaviors using a modified two-dimensional RCSJ model. Our results suggest that multiterminal Josephson junctions are a playground to study highly connected nonlinear networks with novel topologies.

The AC Josephson effect manifests itself in the form of "Shapiro steps" of quantized voltage in Josephson junctions subject to radiofrequency (RF) radiation. This effect presents an early example of a driven-dissipative quantum phenomenon and is presently utilized in primary voltage standards. Shapiro steps have also become one of the standard tools to probe junctions made in a variety of novel materials. Here we study Shapiro steps in a widely tunable graphene-based Josephson junction in which the high-frequency dynamics is determined by the on-chip environment. We investigate the variety of patterns that can be obtained in this well-understood system depending on the carrier density, temperature, RF frequency, and magnetic field. Although the patterns of Shapiro steps can change drastically when just one parameter is varied, the overall trends can be understood and the behaviors straightforwardly simulated, showing some key differences from the conventional RCSJ model. The resulting understanding may help interpret similar measurements in more complex materials.

The search for topological excitations such as Majorana fermions has spurred interest in the boundaries between distinct quantum states. Here, we explore the interface between two prototypical phases of electronic matter with conceptually different ground states, the integer quantum Hall (QH) insulator and the s-wave superconductor (SC). We find clear signatures of chiral Andreev edge states (CAES): hybridized electron and hole states similar to chiral Majorana fermions, which propagate along the QH-SC interface in the direction determined by magnetic field. The interference between the CAES can turn an incoming electron into an outgoing electron or a hole, depending on the phase accumulated by the CAES along the QH-SC interface. Our results demonstrate that these elusive excitations can propagate and interfere over a significant length, opening future possibilities for their coherent manipulation., Main: 3 figures; Supplementary: 12 figures

The vanishing band gap of graphene has long presented challenges for fabricating high-quality quantum point contacts (QPCs) -- the partially transparent p-n interfaces introduced by conventional split-gates tend to short the QPC. This complication has hindered the fabrication of graphene quantum Hall Fabry-P\'erot interferometers, until recent advances have allowed split-gate QPCs to operate utilizing the highly resistive $\nu=0$ state. Here, we present a simple recipe to fabricate QPCs by etching a narrow trench in the graphene sheet to separate the conducting channel from self-aligned graphene side gates. We demonstrate operation of the individual QPCs in the quantum Hall regime, and further utilize these QPCs to create and study a quantum Hall interferometer.

Data for the publication:Nano Lett.2020, 20, 10, 6998–7003

The efficiency of organic solar cells can be increased by careful control of the nanoscale morphology of a dispersed bulk heterojunction device. Atomic force microscopy (AFM) has often been used to characterize morphology but debate persists over the value of traditional AFM measurements since the technique only addresses the active layer topography, and provides insufficient contrast to differentiate between components in a well-mixed composite. Using newer Kelvin Probe Force Microscopy (KPFM) and Quantitative Nanomechanical Mapping (QNM) modes, we demonstrate contrast due to differing elastic modulus and surface potentials between donor and acceptor materials and highlight the value of these techniques to understand critical materials properties as part of a comprehensive nanomorphology study. We test the value of our approach using blends of each of two anilinic squaraines with phenyl-C61-butyric acid methylester. These two squaraine materials differ in chemical compatibility with the standard fullerene acceptor. We vary annealing conditions for our blended films and use the described AFM approaches to demonstrate changing domain sizes, which are affected by chemical compatibility with the fullerene. We demonstrate how KPFM measurements go beyond QNM to provide contrast between materials with reproducibility at a higher image resolution. With the ability to measure contrast between donor and acceptor material, we make a strong case for non-destructive microscopy data to measure effects of variations in annealing temperature on squaraine film morphology, which we confirm influences device performance and efficiency. These conclusions are important for informing material selection for long-term use of associated commercial devices in the field.

This paper presents magnetic interference data from several graphene Josephson junctions. Around the charge neutrality point, an apparent doubling is seen in the period of the interference pattern, similar to what would be expected in a topological junction. The authors eliminate several possible origins of this effect, including SQUID-like contributions from states near the device edges.

We study a two-terminal graphene Josephson junction with contacts shaped to form a narrow constriction, less than 100nm in length. The contacts are made from type II superconducting contacts and able to withstand magnetic fields high enough to reach the quantum Hall (QH) regime in graphene. In this regime, the device conductance is determined by edge states, plus the contribution from the constricted region. In particular, the constriction area can support supercurrents up to fields of ~2.5T. Moreover, enhanced conductance is observed through a wide range of magnetic fields and gate voltages. This additional conductance and the appearance of supercurrent is attributed to the tunneling between counter-propagating quantum Hall edge states along opposite superconducting contacts., 4 pages, 3 figures

Pushing superconductivity to the edge: Physicists make a SQUID using quantum Hall edge states., We present a study of a graphene-based Josephson junction with dedicated side gates carved from the same sheet of graphene as the junction itself. These side gates are highly efficient and allow us to modulate carrier density along either edge of the junction in a wide range. In particular, in magnetic fields in the 1- to 2-T range, we are able to populate the next Landau level, resulting in Hall plateaus with conductance that differs from the bulk filling factor. When counter-propagating quantum Hall edge states are introduced along either edge, we observe a supercurrent localized along that edge of the junction. Here, we study these supercurrents as a function of magnetic field and carrier density.

Establishing ohmic contact to van der Waals semiconductors such as MoS2 is crucial to unlocking their full potential in next-generation electronic devices. Encapsulation of few layer MoS2 with hBN preserves the material's electronic properties but makes electrical contacts more challenging. Progress toward high quality edge contact to encapsulated MoS2 has been recently reported. Here, we evaluate a contact methodology using sputtered MoRe, a Type II superconductor with a relatively high critical field and temperature commonly used to induce superconductivity in graphene. We find that the contact transparency is poor and that the devices do not support a measurable supercurrent down to 3 Kelvin, which has ramifications for future fabrication recipes., Comment: 5 pages, 4 figures

We investigate the electronic properties of ballistic planar Josephson junctions with multiple superconducting terminals. Our devices consist of monolayer graphene encapsulated in boron nitride with molybdenum-rhenium contacts. Resistance measurements yield multiple resonant features, which are attributed to supercurrent flow among adjacent and non-adjacent Josephson junctions. In particular, we find that superconducting and dissipative currents coexist within the same region of graphene. We show that the presence of dissipative currents primarily results in electron heating and estimate the associated temperature rise. We find that the electrons in encapsulated graphene are efficiently cooled through the electron-phonon coupling., 3 Figures, 6 pages

In this study, we examine multiple encapsulated graphene Josephson junctions to determine which mechanisms may be responsible for the supercurrent observed in the quantum Hall (QH) regime. Rectangular junctions with various widths and lengths were studied to identify which parameters affect the occurrence of QH supercurrent. We also studied additional samples where the graphene region is extended beyond the contacts on one side, making that edge of the mesa significantly longer than the opposite edge. This is done in order to distinguish two potential mechanisms: (a) supercurrents independently flowing along both non-contacted edges of graphene mesa, and (b) opposite sides of the mesa being coupled by hybrid electron–hole modes flowing along the superconductor/graphene boundary. The supercurrent appears suppressed in extended junctions, suggesting the latter mechanism.

Coupling superconductors to quantum Hall edge states is the subject of intense investigation as part of the ongoing search for non-abelian excitations. Our group has previously observed supercurrents of hundreds of picoamperes in graphene Josephson junctions in the quantum Hall regime. One of the explanations of this phenomenon involves the coupling of an electron edge state on one side of the junction to a hole edge state on the opposite side. In our previous samples, these states are separated by several microns. Here, a narrow trench perpendicular to the contacts creates counterpropagating quantum Hall edge channels tens of nanometres from each other. Transport measurements demonstrate a change in the low-field Fraunhofer interference pattern for trench devices and show a supercurrent in both trench and reference junctions in the quantum Hall regime. The trench junctions show no enhancement of quantum Hall supercurrent and an unexpected supercurrent periodicity with applied field, suggesting the need for further optimization of device parameters., Comment: 9 pages, 5 figures

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 T→0 the critical current of a long (or short) junction saturates at a level determined by the product of δE (or Δ) and the number of the junction's transversal modes.

Self-assembly of nanoparticles is an important tool in nanotechnology, with numerous applications including thin films, electronics, and drug delivery. We study the deposition of ionic nanoparticles on a glass substrate both experimentally and theoretically. Our theoretical model consists of a stochastic cooperative adsorption and evaporation process on a two-dimensional lattice. By exploring the relationship between the initial concentration of nanoparticles in the colloidal solution and the density of particles deposited on the substrate, we relate the deposition rate of our theoretical model to the concentration., Comment: 7 pages, 6 figures; v2: major revision

We present a class of cooperative sequential adsorption models on a Cayley tree with constant and variable attachment rates and their possible applications for ionic self-assembly of thin films and drug encapsulation of nanoparticles. Using the empty interval method, and generalizing results known from reaction–diffusion processes on Cayley trees, we calculate a variety of quantities such as time-dependent surface coverage and time-dependent probabilities of certain particle configurations.