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

Superconducting diode effect under time-reversal symmetry

In noncentrosymmetric superconductors, superconducting and normal conductions can interchange on the basis of the current flow direction. This effect is termed a superconducting diode effect (SDE), which is a focal point of recent research. The broken inversion and time-reversal symmetry is believed to be the requirements of SDE, but their intrinsic role has remained elusive. Here, we report strain-controlled SDEs in a layered trigonal superconductor, PbTaSe2. The SDE was found exclusively in a strained device with its absence in an unstrained device despite that it is allowed in unstrained trigonal structure. Moreover, the zero-field or magnetic field-even (magnetic field-odd) SDE is observed when the strain and current are along armchair (zigzag) direction The results unambiguously demonstrate the intrinsic SDE under time-reversal symmetry and the critical role of strain-induced electric polarization.

Josephson Diode Effect in Parallel-Coupled Double-Quantum Dots Connected to Unalike Majorana Nanowires

We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin-orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.

Unconventional Superconducting Diode Effects via Antisymmetry and Antisymmetry Breaking

Symmetry breaking plays a pivotal role in unlocking intriguing properties and functionalities in material systems. For example, the breaking of spatial and temporal symmetries leads to a fascinating phenomenon: the superconducting diode effect. However, generating and precisely controlling the superconducting diode effect pose significant challenges. Here, we take a novel route with the deliberate manipulation of magnetic charge potentials to realize unconventional superconducting flux-quantum diode effects. We achieve this through suitably tailored nanoengineered arrays of nanobar magnets on top of a superconducting thin film. We demonstrate the vital roles of inversion antisymmetry and its breaking in evoking unconventional superconducting effects, namely a magnetically symmetric diode effect and an odd-parity magnetotransport effect. These effects are nonvolatilely controllable through in situ magnetization switching of the nanobar magnets. Our findings promote the use of antisymmetry (breaking) for initiating unconventional superconducting properties, paving the way for exciting prospects and innovative functionalities in superconducting electronics.

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.

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.

Intrinsic supercurrent non-reciprocity coupled to the crystal structure of a van der Waals Josephson barrier

Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes that clearly reflects the intrinsic crystal structure of Td-WTe2. The Josephson diode efficiency increases with the Td-WTe2 thickness up to critical thickness, and all junctions, irrespective of the barrier thickness, reveal magneto-chiral characteristics with respect to a mirror plane of Td-WTe2. Our results, together with the twist-angle-tuned magneto-chirality of a Td-WTe2 double-barrier junction, show that two-dimensional materials promise vertical Josephson diodes with high efficiency and tunability.

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.

Enhanced Superconducting Diode Effect due to Coexisting Phases

The superconducting diode effect refers to an asymmetry in the critical supercurrent J_{c}(n[over ^]) along opposite directions, J_{c}(n[over ^])≠J_{c}(-n[over ^]). While the basic symmetry requirements for this effect are known, it is, for junction-free systems, difficult to capture within current theoretical models the large current asymmetries J_{c}(n[over ^])/J_{c}(-n[over ^]) recently observed in experiment. We here propose and develop a theory for an enhancement mechanism of the diode effect arising from spontaneous symmetry breaking. We show-both within a phenomenological and a microscopic theory-that there is a coupling of the supercurrent and the underlying symmetry-breaking order parameter. This coupling can enhance the current asymmetry significantly. Our work might not only provide a possible explanation for recent experiments on trilayer graphene but also pave the way for future realizations of the superconducting diode effect with large current asymmetries.

Parity-conserving Cooper-pair transport and ideal superconducting diode in planar germanium

Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a [Formula: see text] CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with ≈ 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on  the same silicon technology compatible platform.

Phase engineering of anomalous Josephson effect derived from Andreev molecules

A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.

Phase Asymmetry of Andreev Spectra from Cooper-Pair Momentum

In analogy to conventional semiconductor diodes, the Josephson diode exhibits superconducting properties that are asymmetric in applied bias. The effect has been investigated in a number of systems recently, and requires a combination of broken time-reversal and inversion symmetries. We demonstrate a dual of the usual Josephson diode effect, a nonreciprocal response of Andreev bound states to a superconducting phase difference across the normal region of a superconductor-normal-superconductor Josephson junction, fabricated using an epitaxial InAs/Al heterostructure. Phase asymmetry of the subgap Andreev spectrum is absent in the absence of in-plane magnetic field and reaches a maximum at 0.15 T applied in the plane of the junction transverse to the current direction. We interpret the phase diode effect in this system as resulting from finite-momentum Cooper pairing due to orbital coupling to the in-plane magnetic field. At higher magnetic fields, we observe a sign reversal of the diode effect that appears together with a reopening of the spectral gap. Within our model, the sign reversal of the diode effect at higher fields is correlated with a topological phase transition that requires Zeeman and spin-orbit interactions in addition to orbital coupling.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

Tunable Josephson Diode Effect on the Surface of Topological Insulators

The Josephson rectification effect, where the resistance is finite in one direction while zero in the other, has been recently realized experimentally. The resulting Josephson diode has many potential applications on superconducting devices, including quantum computers. Here, we theoretically show that a superconductor-normal metal-superconductor Josephson junction diode on the two-dimensional surface of a topological insulator has large tunability. The magnitude and sign of the diode quality factor strongly depend on the external magnetic field, gate voltage, and the length of the junction. Such rich properties stem from the interplay between different current-phase relations for the multiple transverse transport channels, and can be used for designing realistic superconducting diode devices.

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.