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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.

A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. In this work, we present such a case: we investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in JJs and observe a deviation from the standard CPR. We report on indications of an unexpected breaking of time-reversal symmetry in these devices, detailing the unconventional characteristics that reveal this behavior. These include an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. The analysis examines how multiband effects and the experimentally visualized ferroelectric domain walls give rise to this behavior, giving insight into the Josephson effect in materials that possess ferroelectricity and/or multiband superconductivity.

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.

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 work, we report on hot carrier diffusion in graphene across large enough length scales that the carriers are not thermalized across the crystal. The carriers are injected into graphene at one site and their thermal transport is studied as a function of applied power and distance from the heating source, up to tens of micrometers away. Superconducting contacts prevent out-diffusion of hot carriers to isolate the electron-phonon coupling as the sole channel for thermal relaxation. As local thermometers, we use the amplitude of the universal conductance fluctuations, which varies monotonically as a function of temperature. By measuring the electron temperature simultaneously along the length we observe a thermal gradient which results from the competition between electron-phonon cooling and lateral heat flow.

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.