Multiterminal Inverse AC Josephson Effect

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.

Nonreciprocal Josephson Linear Response

We consider the finite-frequency response of multiterminal Josephson junctions and show how nonreciprocity in them can show up at linear response, in contrast to the static Josephson diodes featuring nonlinear nonreciprocity. At finite frequencies, the response contains dynamic contributions to the Josephson admittance, featuring the effects of Andreev bound state transitions along with Berry phase effects, and reflecting the breaking of the same symmetries as in Josephson diodes. We show that outside exact Andreev resonances, the junctions feature nonreciprocal reactive response. As a result, the microwave transmission through those systems is nondissipative, and the electromagnetic scattering can approach complete nonreciprocity. Besides providing information about the nature of the weak link energy levels, the nonreciprocity can be utilized to create nondissipative and small-scale on-chip circulators whose operation requires only rather small magnetic fields.

Phase-engineering the Andreev band structure of a three-terminal Josephson junction

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

Gate-tunable superconducting diode effect in a three-terminal Josephson device

The phenomenon of non-reciprocal critical current in a Josephson device, termed the Josephson diode effect, has garnered much recent interest. Realization of the diode effect requires inversion symmetry breaking, typically obtained by spin-orbit interactions. Here we report observation of the Josephson diode effect in a three-terminal Josephson device based upon an InAs quantum well two-dimensional electron gas proximitized by an epitaxial aluminum superconducting layer. We demonstrate that the diode efficiency in our devices can be tuned by a small out-of-plane magnetic field or by electrostatic gating. We show that the Josephson diode effect in these devices is a consequence of the artificial realization of a current-phase relation that contains higher harmonics. We also show nonlinear DC intermodulation and simultaneous two-signal rectification, enabled by the multi-terminal nature of the devices. Furthermore, we show that the diode effect is an inherent property of multi-terminal Josephson devices, establishing an immediately scalable approach by which potential applications of the Josephson diode effect can be realized, agnostic to the underlying material platform. These Josephson devices may also serve as gate-tunable building blocks in designing topologically protected qubits.

Supercurrent in Bi4Te3 Topological Material-Based Three-Terminal Junctions

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi4Te3 and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators' weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current-phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents.

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.

Targeted modifications of monolithic multiterminal superconducting weak-links

In a multi-branch metallic interconnect we demonstrate the possibility to induce targeted modifications of the material properties by properly selecting the intensity and polarity of the applied current. We illustrate this effect in Y-shape multiterminal devices made of Nb on sapphire for which we show that the superconducting critical current can be lowered in a controlled manner at a preselected junction. We further observe the gradual appearance of Fraunhofer-like critical current oscillations with magnetic field which indicates the gradual modification of a superconducting weak link. This method permits progressive modifications of a hand-picked junction without affecting the neighboring terminals. The proposed approach has the benefit of being inexpensive and requiring conventional electronics. This technique represents a major step toward all-electric control of multiterminal Josephson junctions.