Multiterminal Josephson Junction Research Articles

Mapping the Topological Proximity-Induced Gap in Multiterminal Josephson Junctions

Mapping the Topological Proximity-Induced Gap in Multiterminal Josephson Junctions

Evidence for π-Shifted Cooper Quartets and Few-Mode Transport in PbTe Nanowire Three-Terminal Josephson Junctions.

Josephson junctions are typically characterized by a single phase difference across two superconductors. This conventional two-terminal Josephson junction can be generalized to a multiterminal device where the Josephson energy contains terms with contributions from multiple independent phase variables. Such multiterminal Josephson junctions (MTJJs) are being considered as platforms for engineering effective Hamiltonians with nontrivial topologies, such as Weyl crossings and higher-order Chern numbers. These prospects rely on the ability to create MTJJs with nonclassical multiterminal couplings in which only a few quantum modes are populated. Here, we demonstrate these requirements in a three-terminal Josephson junction fabricated on selective-area-grown (SAG) PbTe nanowires. We observe signatures of a π-shifted Josephson effect, consistent with interterminal couplings mediated by four-particle quantum states called Cooper quartets. We further observe a supercurrent coexistent with a non-monotonic evolution of the conductance with gate voltage, indicating transport mediated by a few quantum modes in both two- and three-terminal devices.

Universality of the Spectra of Multiterminal Josephson Junction

Andreev bound states are formed in multiterminal structures based on normal metals and superconductors. Their spectrum is determined by the system parameters, in particular the scattering phases and transmission coefficients at the nodes. The article found conditions under which Andreev bound states are universal: they don’t change with any change in the reflection phases. As a consequence, the spectrum is completely determined by the transport characteristics of the system. The result was obtained for a structure in the form of a normal metal M-finite star, each of the rays (terminals) Nk of which is in contact with its superconductor Sk, 1 ≤ k ≤ M. Together they form a multiterminal Josephson junction. At the center of the structure there is a non-magnetic impurity with its some scattering matrix.

Self-heating effects and switching dynamics in graphene multiterminal Josephson junctions

We experimentally investigate the electronic transport properties of a three-terminal graphene Josephson junction. We find that self-heating effects strongly influence the behavior of this multiterminal Josephson junction (MTJJ) system. We show that existing simulation methods based on resistively and capacitively shunted Josephson junction networks can be significantly improved by taking into account these heating effects. We also investigate the phase dynamics in our MTJJ by measuring its switching current distribution and find correlated switching events in different junctions. We show that the switching dynamics is governed by phase diffusion at low temperatures. Furthermore, we find that self-heating introduces additional damping that results in overdamped I−V characteristics when normal and supercurrents coexist in the device. Published by the American Physical Society 2024

Quartet tomography in multiterminal Josephson junctions

Quartet tomography in multiterminal Josephson junctions

Quantum Circuits with Multiterminal Josephson-Andreev Junctions

We explore superconducting quantum circuits where several leads are simultaneously connected beyond the tunneling regime, such that the fermionic structure of Andreev bound states in the resulting multiterminal Josephson junction influences the states of the full circuit. Using a simple model of single-channel contacts and a single level in the middle region, we discuss different circuit configurations where the leads are islands with finite capacitance and/or form loops with finite inductance. We find situations of practical interest where the circuits can be used to define noise-protected qubits, which map to the bifluxon and 0−π qubits in the tunneling regime. We also point out the subtleties of the gauge choice for a proper description of these quantum circuit dynamics. Published by the American Physical Society 2024

Hidden Symmetry in Interacting-Quantum-Dot-Based Multiterminal Josephson Junctions.

We study a multiterminal Josephson junction based on an interacting quantum dot coupled to n superconducting BCS leads. Using an Anderson type model of a local level with an arbitrary on-site Coulomb repulsion, we uncover its surprising equivalence with an effective two-terminal junction with symmetric couplings to appropriately phase-biased leads. Regardless of the strength of the Coulomb interaction, this hidden symmetry enables us to apply well-established numerical and theoretical tools for exact evaluation of various physical quantities, and imposes strict relations among them. Focusing on three-terminal devices, we then demonstrate several phenomena such as the existence of the finite energy band crossings and superconducting transistor and diode effects, as well as current phase relation modulation.

Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction.

We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.

Magnetic-field-free nonreciprocal transport in graphene multiterminal Josephson junctions

Magnetic-field-free nonreciprocal transport in graphene multiterminal Josephson junctions

Ground state topology of a four-terminal superconducting double quantum dot

In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.

Andreev processes in mesoscopic multiterminal graphene Josephson junctions

There is growing interest in using multi-terminal Josephson junctions (MTJJs) as a platform to artificially emulate topological phases and to investigate complex superconducting mechanisms such as quartet and multiplet Cooper pairings. Current experimental signatures in MTJJs have led to conflicting interpretations of the salient features. In this work, we report a collaborative experimental and theoretical investigation of graphene-based four-terminal Josephson junctions. We observe resonant features in the differential resistance maps that resemble those ascribed to multiplet Cooper pairings. To understand these features, we model our junctions using a circuit network of coupled two-terminal resistively and capacitively shunted junctions (RCSJs). Under appropriate bias current, the model predicts that a current flowing between two diagonal terminals in a four-terminal geometry may be represented as a sinusoidal function of a weighted sum of the superconducting phases. We show that starting from a semi-classical model with diffusive current-phase relations, the MTJJ effectively emulates a general form of the expected current-phase relation for multiplet Cooper pairings. Our study therefore suggests that differential resistance measurements alone are insufficient to conclusively distinguish resonant Andreev reflection processes from semi-classical circuit-network effects.

Weyl singularities in polaritonic multiterminal Josephson junctions

We study theoretically analog multi-terminal Josephson junctions formed by gapped superfluids created upon resonant pumping of cavity exciton-polaritons. We study the $p$-like bands of a 5-terminal junction in the 4D parameter space created by the superfluid phases acting as quasi-momenta. We find 4/6 Weyl points in 3D subspaces with preserved/broken time-reversal symmetry. We link the real space topology (vortices) to the parameter space one (Weyl points). We derive an effective Hamiltonian encoding the creation, motion, and annihilation of Weyl nodes in 4D. Our work paves the way to the study of exotic topological phases in a platform allowing direct measurement of eigenstates and band topology.

Multi-terminal Josephson junctions: A road to topological flux networks

Multi-terminal Josephson junctions were recently proposed as a versatile and tunable platform to emulate topological Bloch-like Hamiltonians in arbitrary dimensions. In this perspective article, we will give a brief overview of the subject and recognize these mesoscopic devices as realizations of topological flux networks as the ones envisioned by Avron and coworkers in their seminal works on the early days of the quantum Hall effect. We summarize the current state-of-the-art theoretical and experimental research regarding these Josephson devices, highlighting recent developments and giving an outlook on current trends.

Probing the topological band structure of diffusive multiterminal Josephson junction devices with conductance measurements

The energy of an Andreev bound state in a clean normal metal in contact with two superconductors disperses with the difference Δϕ in the superconducting phase between the superconductors in much the same way as the energies of electrons in a one-dimensional crystal disperse with the crystal momentum k of the electrons. A normal metal with n superconductors maps onto a n − 1 dimensional crystal, each dimension corresponding to the phase difference Δϕi between a specific pair of superconductors. The resulting band structure as a function of the phase differences {Δϕi} in such ballistic devices has been proposed to have a topological nature with gapped regions characterized by different Chern numbers separated by regions where the gap in the quasiparticle spectrum closes. A similar complex evolution of the quasiparticle spectrum with {Δϕi} has also been predicted for diffusive normal metals in contact with multiple superconductors. While the underlying topological description is different in diffusive devices, gapped regions of the band diagram associated with different topological indices are also separated by regions where the gap closes. Here, we show that the variation of the density of states at the Fermi energy of such a system can be directly probed by relatively simple conductance measurements, allowing rapid characterization of the energy spectrum.

Phase dynamics in an AC-driven multiterminal Josephson junction analog

In the presence of an AC drive, multiterminal Josephson junctions exhibit the inverse AC Josephson effect, where the oscillations of the superconducting phase of each junction can lock onto one another or onto the external drive. The competition between these different phase locked states results in a complex array of quantized voltage plateaus whose stability strongly depend on the circuit parameters of the shunted junctions. This phase diagram cannot be explored with low temperature transport experiments alone, given the breadth of the parameter space, so we present an easily tunable analog circuit whose dynamical properties emulate those of a three terminal junction. We focus on the observation of the multiterminal inverse AC Josephson effect, and we discuss how to identify Shapiro steps associated with each of the three junctions as well as their quartet states. We only observe integer phase locked states in strongly overdamped networks, but fractional Shapiro steps appear as well when the quality factor of the junctions increases. Finally, we discuss the role of transverse coupling in the synchronization of the junctions.

Selective control of conductance modes in multi-terminal Josephson junctions

The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of a multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work, we employ a quantum point contact geometry in three-terminal Josephson devices to demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presence of superconducting coupling. These results establish a full platform on which to realize tunable Andreev bound state spectra in multi-terminal Josephson junctions.

Dynamical Stabilization of Multiplet Supercurrents in Multiterminal Josephson Junctions.

The dynamical properties of multiterminal Josephson junctions (MT-JJs) have 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. Here, we show that multiplet resonances can also emerge as a consequence of the three-terminal circuit model. The supercurrent appears due to correlated phase dynamics at values that correspond to the multiplet condition nV1 = -mV2 of applied bias. Multiplet resonances are seen in nanofabricated three-terminal graphene JJs, analog three-terminal JJ circuits, and circuit simulations. The stabilization of the supercurrent is purely dynamical, and a close analog to Kapitza's inverted pendulum problem. We describe parameter considerations that optimize the detection of the multiplet lines both for design of future devices.

Selective Control of Conductance Modes in Multi-terminal Josephson Junctions

Selective Control of Conductance Modes in Multi-terminal Josephson Junctions

Non-Abelian monopoles in the multiterminal Josephson effect

In this work we present a detailed theoretical analysis for the spectral properties of Andreev bound states in the multiterminal Josephson junctions by employing a symmetry-constrained scattering matrix approach. We find that in the synthetic multidimensional space of superconducting phases, crossings of Andreev bands may support non-Abelian SU(2) monopoles with a topological charge characterized by the second class Chern number. We propose that these topological defects can be detected via a nonlinear response measurement of the current autocorrelations. In addition, multiterminal Josephson junction devices can be tested as a hardware platform for realizing holonomic quantum computation.

Multiterminal ballistic Josephson junctions coupled to normal leads

Multiterminal Josephson junctions have aroused considerable theoretical interest recently and numerous works aim at putting the predictions of correlations among Coopers (i.e., the so-called quartets) and simulation of topological matter to the test of experiments. This paper is motivated by recent experimental investigation from the Harvard group reporting $h/4e$-periodic quartet signal in a four-terminal configuration containing a loop pierced by magnetic flux, together with inversion controlled by the bias voltage, i.e., the quartet signal can be larger at half-flux quantum than in zero magnetic field. Here, we theoretically focus on devices consisting of finite-size quantum dots connected to four superconducting leads and to a normal lead. In addition to presenting numerical calculations of the quartet signal within a simplified modeling, we reduce the device to a non-Hermitian Hamiltonian in the infinite-gap limit. Then, relaxation has the surprising effect of producing sharp peaks and log-normal variations in the voltage sensitivity of the quartet signal in spite of the expected moderate fluctuations in the two-terminal DC Josephson current. The phenomenon is reminiscent of a resonantly driven harmonic oscillator having amplitude inverse proportional to the damping rate, and of the thermal noise of a superconducting weak link, inverse proportional to the Dynes parameter. Perspectives involve quantum bath engineering multiterminal Josephson junctions in the circuits of cavity quantum electrodynamics.