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Multiterminal Josephson junctions are a promising platform to host synthetic topological phases of matter and Floquet states. However, the energy scales governing topological protection in these devices are on the order of the spacing between Andreev bound states. Recent theories suggest that similar phenomena may instead be explored in circuits composed of two-terminal Josephson junctions, allowing for the topological protection to be controlled by the comparatively large Josephson energy. Here, we explore a Josephson circuit, in which three superconducting electrodes are connected through Josephson junctions to a common superconducting island. We demonstrate the dynamic generation of multiplet resonances, which have previously been observed in multiterminal Josephson junctions. The multiplets are found to be robust to elevated temperatures and are confirmed by exhibiting the expected Shapiro step quantization under a microwave drive. We also find an unexpected novel supercurrent, which couples a pair of contacts that are both voltage-biased with respect to the common superconducting island. We show that this supercurrent results from synchronization of the phase dynamics and pose the question whether it should also carry a topological contribution.

Increasing the density of superconducting circuits requires compact components, however, superconductor-based capacitors typically perform worse as dimensions are reduced due to loss at surfaces and interfaces. Here, parallel plate capacitors composed of aluminum-contacted, crystalline silicon fins are shown to be a promising technology for use in superconducting circuits by evaluating the performance of lumped element resonators and transmon qubits. High aspect ratio Si-fin capacitors having widths below $300nm$ with an approximate total height of 3$\mu$m are fabricated using anisotropic wet etching of Si(110) substrates followed by aluminum metallization. The single-crystal Si capacitors are incorporated in lumped element resonators and transmons by shunting them with lithographically patterned aluminum inductors and conventional $Al/AlO_x/Al$ Josephson junctions respectively. Microwave characterization of these devices suggests state-of-the-art performance for superconducting parallel plate capacitors with low power internal quality factor of lumped element resonators greater than 500k and qubit $T_1$ times greater than 25$\mu$s. These results suggest that Si-Fins are a promising technology for applications that require low loss, compact, superconductor-based capacitors with minimal stray capacitance.

An important route of engineering topological states and excitations is to combine superconductors (SC) with the quantum Hall (QH) effect, and over the past decade, significant progress has been made in this direction. While typical measurements of these states focus on electronic properties, little attention has been paid to the accompanying thermal responses. Here, we examine the thermal properties of the interface between a type-II superconducting electrodes and graphene in the QH regime. We use the thermal noise measurement to probe the local electron temperature of the biased interface. Surprisingly, the measured temperature raise indicates that the superconductor provides a significant thermal conductivity, which is linear in temperature. This suggests electronic heat transport and may be unexpected, because the number of the quasiparticles in the superconductor should be exponentially suppressed. Instead, we attribute the measured electronic heat conductivity to the overlap of the normal states in the vortex cores., Comment: Lingfei Zhao, Trevyn F.Q. Larson and Zubair Iftikhar contributed equally to this work

There has been a growing interest in hybrid quantum Hall (QH) superconductor devices, driven by the prospect to realize exotic ground states and excitations with non-abelian exchange statistics. While the existing experiments clearly demonstrate Andreev coupling between the edge states and the superconductors, the question remains whether the quantum coherence could propagate between several superconducting contacts via chiral channels. To answer this question, we have first extended the Landauer-B\"uttiker (LB) formalism to samples with one superconducting contact and found a remarkable agreement within a series of measurements related to each other via LB-type formulae. We have then switched to the case of multiple superconducting contacts, and found that we can describe the measurements self-consistently if we neglect the superconducting phase coherence between multiple contacts. We interpret this result as a negative answer to the question posed above: the phase correlations between multiple superconducting contacts are not established via micron-long quantum Hall edge states. Looking forward, our approach may find applications in the broader field of topological superconductivity and proximal structures. Possible violations of the self-consistency tests presented here may be used as an indication that superconducting phase coherence is induced in the quantum Hall edges.

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose degrees of freedom are either magnetic fluxes or electric charges in the circuit. By combining nonlinear circuit elements (such as Josephson junctions or quantum phase slips), it is possible to build circuits where a standard Lagrangian description (and thus the standard quantization method) does not exist. Inspired by the mathematics of symplectic geometry and graph theory, we address this challenge, and present a Hamiltonian formulation of non-dissipative electrodynamic circuits. The resulting procedure for circuit quantization is independent of whether circuit elements are linear or nonlinear, or if the circuit is driven by external biases. We explain how to re-derive known results from our formalism, and provide an efficient algorithm for quantizing circuits, including those that cannot be quantized using existing methods., Comment: 30 pages, 8 figures

Under a high frequency drive, Josephson junctions demonstrate "Shapiro steps" of quantized voltage. These are dynamically stabilized states, in which the phase across the junction locks to the external drive. We explore the stochastic switching between two symmetric steps at $\frac{\hbar\omega}{2e}$ and $-\frac{\hbar\omega}{2e}$. Surprisingly, the switching rate exhibits a pronounced non-monotonicity as a function of temperature, violating the general expectation that transitions should become faster with temperature. We explain this behavior by realizing that the system retains memory of the dynamic state from which it is switching, thereby breaking the conventional simplifying assumptions about separations of time scales.

We perform a systematic study of Andreev conversion at the interface between a superconductor and graphene in the quantum Hall (QH) regime. We find that the probability of Andreev conversion from electrons to holes follows an unexpected but clear trend: the dependencies on temperature and magnetic field are nearly decoupled. We discuss these trends and the role of the superconducting vortices, whose normal cores could both absorb and dephase the individual electrons in a QH edge. Our study may pave the road to engineering future generation of hybrid devices for exploiting superconductivity proximity in chiral channels.

Superconducting diodes are proposed non-reciprocal circuit elements that should exhibit non-dissipative transport in one direction while being resistive in the opposite direction. Multiple examples of such devices have emerged in the past couple of years, however their efficiency is typically limited, and most of them require magnetic field to function. Here we present a device achieving efficiencies upwards of 90% while operating at zero field. Our samples consist of a network of three graphene Josephson junctions linked by a common superconducting island, to which we refer as a Josephson triode. The triode is tuned by applying a control current to one of the contacts, thereby breaking the time-reversal symmetry of the current flow. The triode's utility is demonstrated by rectifying a small (tens of nA amplitude) applied square wave. We speculate that devices of this type could be realistically employed in the modern quantum circuits., Comment: 11 pages, 9 figures

The vanishing band gap of graphene has long presented challenges for making 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.

The dynamical properties of multi-terminal Josephson junctions have recently attracted interest, driven by the promise of new insights into synthetic topological phases of matter and Floquet states. This effort has culminated in the discovery of Cooper multiplets, in which the splitting of a Cooper pair is enabled via a series of Andreev reflections that entangle four (or more) electrons. In this text, we show conclusively that multiplet resonances can also emerge as a consequence of the three terminal circuit model. The supercurrent appears due to the correlated phase dynamics at values that correspond to the multiplet condition $nV_1 = -mV_2$ of applied bias. The emergence of multiplet resonances is seen in i) a nanofabricated three-terminal graphene Josephson junction, ii) an analog three terminal Josephson junction circuit, and iii) a circuit simulation. The mechanism which stabilizes the state of the system under those conditions is purely dynamical, and a close analog to Kapitza's inverted pendulum problem. We describe parameter considerations that best optimize the detection of the multiplet lines both for design of future devices. Further, these supercurrents have a classically robust $\cos2\phi$ energy contribution, which can be used to engineer qubits based on higher harmonics.

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 multi-terminal 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 multi-terminal Josephson junctions are a playground to study highly-connected nonlinear networks with novel topologies., Comment: 11 pages, 7 figures

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