The escalating energy consumption of large computation facilities, exceeding 100 MW, motivates the exploration of energy-efficient alternatives. Superconducting (SC) electronics offer a promising solution by eliminating resistive losses and significantly enhancing operational speed due to the absence of RC time constant limitations. The potential for THz-range clock frequencies in many superconductors opens the door to computing speeds several orders of magnitude faster than current semiconductor technologies, sparking renewed interest in developing digital SC computers. One critical component for such computers is the diode. Its nonreciprocal current-voltage (I-V) characteristic is essential for signal processing and AC-DC conversion, and forms a building block for Boolean logic. Superconducting diodes require strongly asymmetric critical currents (Ic+ ≠ Ic−). While spatially asymmetric SC devices can exhibit nonreciprocity, most previous demonstrations require finite magnetic fields, unlike the zero-field operation needed for computer components. Zero-field nonreciprocity is typically forbidden by time-reversal symmetry. Recent research explored nonreciprocity induced by spin-orbit interaction (SOI) in noncentrosymmetric superconductors, but these methods often still require significant magnetic fields. This work focuses on developing SC diodes exhibiting large and switchable nonreciprocity at zero magnetic field. The approach leverages the combination of a self-field effect from asymmetric bias and stray fields from a trapped Abrikosov vortex (AV) to achieve this zero-field operation. The researchers demonstrate that the critical current ratio (Ic+/Ic−) can reach an order of magnitude, with rectification efficiency exceeding 70%. Furthermore, the ability to switch nonreciprocity on/off and change diode polarity via vortex manipulation and bias configuration introduces memory functionality. This opens possibilities for a new generation of superconducting in-memory computers.

Existing research on superconducting diodes and rectifiers has largely focused on spatially asymmetric structures or those operating under finite magnetic fields. Early work demonstrated SC diodes based on spatially nonuniform Josephson junctions (JJs). Studies of SC ratchets, rectifying the motion of Josephson or Abrikosov vortices, have also been extensive. However, these approaches primarily function in the presence of external magnetic fields. The constraint of time-reversal symmetry in zero-field scenarios necessitates breaking both space and time-reversal symmetries for zero-field SC diode operation. Recent investigations have examined nonreciprocity induced by spin-orbit interaction (SOI) in noncentrosymmetric superconductors, but these approaches generally require substantial magnetic fields. Several works reported zero-field SC diode operation, incorporating additional effects. This research highlights nonreciprocity as a tool for studying unconventional superconductors.

The study employs a two-pronged approach: (i) utilizing a nonuniform bias to achieve nonreciprocity at finite fields and (ii) shifting this nonreciprocity to zero field using persistent stray fields from a trapped AV. The simplest case involves a short JJ (length L < λJ, where λJ is the Josephson penetration depth), simplifying analysis by neglecting screening effects and Josephson vortices. Numerical modeling simulates the I(Φ) modulation (critical current versus magnetic flux) for various scenarios: a uniform JJ, a JJ with nonuniform bias (leading to a self-field effect), and a JJ with both nonuniform bias and nonuniform critical current density. These simulations reveal that nonuniformities break spatial symmetry, leading to nonreciprocity at finite fields but retaining centrosymmetry. The introduction of a trapped AV breaks space-reversal symmetry while preserving time-reversal symmetry for short JJs, creating a flux offset. Further simulations investigate the combined effects of nonuniformity and stray magnetic fields from a trapped AV. The simulations reveal that the nonreciprocal peaks gradually shift towards zero field with decreasing distance between the AV and the JJ, enabling optimal geometrical configuration for zero-field diode operation. Experimental verification involves four-terminal cross-like JJs fabricated using two types of devices: D1 (Nb(70 nm)/CuNi(50 nm) bilayer with superparamagnetic CuNi) and D2 (single Nb(70nm) film), creating either proximity-coupled Nb-CuNi-Nb JJs or Nb-c-Nb JJs. These cross-like structures permit controllable introduction of bias asymmetry, affecting self-field generation and influencing junction characteristics. Measurements of I(H) patterns for both devices with different bias configurations (straight bias, right-corner bias, left-corner bias) demonstrate the effect of self-fields in inducing nonreciprocity at finite fields. The I-V characteristics at different magnetic fields showcase the large nonreciprocity achievable. To explore diode performance, the study examines the effect of introducing a trapped AV or antivortex (controllably introduced/removed by current pulses). I(H) modulations, nonreciprocity, and rectified DC voltage are analyzed for both JJs in D1, revealing significant nonreciprocity and rectification at zero field in the presence of the vortex or antivortex. The diode polarity can be switched by changing either the vortex sign or bias configuration. The study also investigates the amplitude dependence of rectification for both D1 and D2. Numerical simulations using a model accounting for self-field effects and vortex-induced phase shifts are used to analyze the results, showing that the simulated results match the experimental observations quite well. The model also allows for predicting the performance improvements for future designs. The key parameters used in simulations include self-field inductance and the vorticity of the trapped AV.

The research demonstrates the successful operation of superconducting Josephson diodes-with-memory, characterized by large and switchable nonreciprocity at zero magnetic field. The key findings are summarized as follows: 1. **High Nonreciprocity:** The measured nonreciprocity of critical current surpasses a factor of 4 at zero field and exceeds an order of magnitude at finite fields. Numerical modeling suggests potential for further improvements in nonreciprocity by an additional order of magnitude via optimized design. 2. **High Rectification Efficiency:** Rectification efficiency surpasses 70% at zero field, demonstrating the suitability of these diodes for more complex logical Boolean operations required in digital superconducting computers. 3. **Switchability and Tunability:** A unique feature of these diodes is their switchable and tunable nature. Nonreciprocity at H=0 can be easily introduced/removed through trapping/removing Abrikosov vortices, and diode polarity is flipped by either changing the vortex sign or the bias configuration. This switchability is fundamental to the memory functionality, allowing three distinct states at H=0: a reciprocal state ('0', without AV), and states '+1' and '-1' with positive and negative polarities. 4. **Memory Functionality:** The ability to switch between different diode states ('0', '+1', '-1') using vortex manipulation enables in-memory operation, potentially circumventing data-shuffling bottlenecks in conventional computing architectures. 5. **Experimental Validation:** The experimental findings corroborate the numerical modeling, verifying the concept of achieving zero-field nonreciprocity via the combined effects of nonuniform bias and trapped Abrikosov vortices. The experimental demonstration uses conventional Nb-technology, indicating scalability for large-scale applications. 6. **Device Characterization:** The devices used in the study, D1 (Nb-CuNi-Nb junctions) and D2 (Nb-c-Nb junctions), exhibit similar behavior, with D2 showing advantages due to higher IcRn values.

The successful demonstration of superconducting diodes with large, switchable nonreciprocity at zero magnetic field addresses a significant challenge in the development of digital superconducting computers. The ability to operate without external magnetic fields is crucial for practical applications and simplifies the design of complex circuits. The high rectification efficiency and switchable polarity, combined with the memory functionality, opens opportunities for advanced computing paradigms, particularly in-memory computing. The use of conventional Nb-technology enhances the feasibility of scaling up these devices for practical applications. The significant difference in Ic+/Ic− demonstrates the potential of the device to perform rectification at zero magnetic field. Further improvements could be explored through designing the geometry and improving junction characteristics. The results have significant implications for advancing superconducting electronics and developing next-generation computing architectures. The memory functionality offered by the switchable diode design could significantly improve energy efficiency and reduce data-transfer bottlenecks, potentially leading to significant performance enhancements in future superconducting computers.

This work successfully demonstrated the operation of high-performance superconducting Josephson diodes with integrated memory functionality, operating at zero magnetic field. The diodes exhibit significant nonreciprocity and rectification efficiency, exceeding 70%, and their switchable nature is achieved through manipulating trapped Abrikosov vortices. This novel approach offers a promising path towards the development of energy-efficient, high-speed in-memory superconducting computers. Future research could explore further optimization of device geometry, materials, and integration into complex circuit architectures to fully realize the potential of this technology.

While the study demonstrates significant advancements, some limitations should be acknowledged. The current device design is based on specific geometric parameters and material properties, which may need to be further optimized for broader applicability. The long-term stability of the trapped Abrikosov vortices and their susceptibility to thermal fluctuations could affect device reliability in real-world applications. More extensive studies on device scalability and integration into complex circuits are needed before large-scale deployment is possible.