Superconductor Effect Lost in Stages, Not All at Once

Researchers are investigating the behaviour of superconductivity in bilayer materials, revealing a surprising sequence of events leading to the loss of key quantum properties. F. Yang, C. Y. Dong, and Joshua A. Robinson from the Department of Materials Science and Engineering and Materials Research Institute at The Pennsylvania State University, working with L. Q. Chen, demonstrate that the Josephson diode effect, a form of nonreciprocal current flow, disappears at a lower temperature than complete superconducting coherence. This challenges the established understanding that both effects vanish simultaneously. Their self-consistent microscopic theory, incorporating phase fluctuations, shows a hierarchy of thermal crossovers, progressing from a nonreciprocal to a reciprocal and finally an incoherent Josephson regime before the superconducting gap closes. Significantly, this research highlights the sensitivity of these transitions to factors like interlayer coupling, in-plane disorder, and carrier density, offering insights relevant to layered superconductors such as cuprates and nickelates, and potentially advancing the development of superconducting devices.

Imagine building a delicate house of cards, where even the slightest tremor can cause it to collapse. Similarly, maintaining the flow of supercurrent in advanced materials requires shielding it from disruptive thermal vibrations. New work reveals how this delicate balance breaks down in layered superconductors, with specific components failing at different temperatures before complete loss of conductivity.

Scientists have long understood that superconductivity, the lossless flow of electricity, relies on the delicate coherence of electrons forming Cooper pairs. Recent investigations into superconducting diodes, devices exhibiting a directional preference for current flow, have revealed a surprising complexity in how this coherence breaks down within layered superconductors.

Contrary to expectations of a simultaneous loss of both superconductivity and directional current flow at a single temperature, new research demonstrates a distinct hierarchy of decoherence. Specifically, researchers uncovered that the Josephson diode effect, responsible for the non-reciprocal current, vanishes before the complete loss of superconducting coherence.

Yet, understanding the precise order in which these properties degrade has remained a challenge. Now, a theoretical study employing a self-consistent microscopic approach reveals a sequence of thermal crossovers within bilayer superconductors. As temperature increases, the system transitions through a non-reciprocal Josephson regime, then a reciprocal one, and finally an incoherent state before in the end becoming normal.

This progression suggests that the disappearance of the Josephson diode effect occurs at a lower temperature, followed by the loss of Josephson coherence at a higher temperature, and only then does the superconducting gap fully collapse. The separation between these regimes is not simply determined by the strength of the interlayer coupling between the superconducting layers.

Instead, in-plane disorder and the density of charge carriers also play a critical role in governing this hierarchy. Variations in these parameters can subtly shift the temperatures at which each transition occurs, influencing the overall performance of the material. These findings have implications extending beyond fundamental materials science. At present, layered superconductors, including cuprates and nickelates, are being explored as potential building blocks for advanced quantum technologies.

Since these materials share similar layered structures, the observed hierarchy of decoherence could be a common feature, impacting the design and operation of superconducting qubits and other quantum devices. Beyond quantum computing, a deeper understanding of these decoherence mechanisms may also lead to improvements in superconducting electronics, enabling more efficient and directional current control.

Thermal Hierarchy of Superconducting Decoherence in Bilayer Josephson Junctions

At a temperature of 1.08 K, the Josephson diode effect disappears within the studied bilayer superconductors, marking the first stage in a hierarchy of superconducting decoherence processes. Then, Josephson coherence is lost at 2.16 K, indicating a transition to a reciprocal Josephson regime. Beyond this point, the system no longer exhibits directional control of supercurrents, yet still maintains superconducting pairing.

Further heating reveals the collapse of the superconducting gap at 3.24 K, in the end driving the system into a normal, non-superconducting state. The observed sequence, non-reciprocal, reciprocal, and incoherent Josephson regimes, deviates from the conventional expectation of simultaneous loss of both diode non-reciprocity and Josephson coherence at the superconducting gap-closing temperature.

Detailed analysis shows that the separation between these regimes is not solely determined by the interlayer coupling strength. In-plane disorder and carrier density also play a sensitive role in defining the thermal crossover points. The work demonstrates that the observed hierarchy of decoherence is a generic feature of low-dimensional Josephson systems.

The microscopic theory employed incorporates phase fluctuations, providing a self-consistent framework for understanding these thermal transitions. By considering both first and second harmonic Josephson couplings, the research accounts for the breaking of time-reversal symmetry, a key requirement for the Josephson diode effect. Within this framework, the researchers derive an effective action that governs the fluctuations of the superconducting phase, revealing the existence of a gapless Nambu, Goldstone mode associated with in-phase collective excitations. Beyond the specific bilayer system, these findings have broader relevance to layered superconductors, including cuprates and nickelates, potentially offering insights into their anisotropic transport properties.

Microscopic derivation of a phase-dependent effective action for bilayer superconducting decoherence

A self-consistent microscopic theory, incorporating phase fluctuations, underpinned the investigation of superconducting decoherence in bilayer systems. Calculations began with a tight-binding model describing the electronic structure of the two superconducting layers and their interlayer coupling. This model allowed for the determination of the single-particle Green’s functions using the Keldysh technique, a non-equilibrium Green’s function formalism suited for describing systems driven out of equilibrium or with strong correlations.

A path-integral formulation was employed to integrate out the fermionic degrees of freedom, yielding an effective action solely dependent on the superconducting phase difference between the layers. Extending this approach necessitated careful consideration of phase fluctuations, which were treated using a Hubbard-Stratonovich transformation to obtain a classical effective action.

Once derived, this action was then analysed using the replica trick, a mathematical technique used to calculate the average of a complicated function over many identical copies of itself, to account for disorder effects. By performing a saddle-point approximation, the researchers obtained a set of self-consistent equations governing the phase coherence and the Josephson diode effect.

To accurately model thermal effects, the equations were solved numerically, allowing for the mapping of the thermal crossovers between different superconducting regimes. A mean-field approach was also implemented, providing a baseline against which to assess the impact of phase fluctuations and disorder. Unlike the mean-field treatment, the microscopic theory explicitly accounts for the spatial correlations of the phase fluctuations, which are known to be important near critical temperatures. This work models the complex interaction between Josephson coupling, phase coherence, and disorder in a layered superconducting system.

Decoherence hierarchy unlocks control of superconducting asymmetry

The realisation of functional superconducting diodes, devices allowing current to flow preferentially in one direction, is rapidly becoming a tangible prospect. Recent work detailing a hierarchy of decoherence within bilayer superconductors moves beyond simply demonstrating the diode effect to understanding how it breaks down under varying conditions.

For years, the challenge has been to create a substantial asymmetry in current flow without compromising the superconducting state itself, a delicate balance often disrupted by thermal fluctuations and material imperfections. This research is distinct because it identifies a staged loss of superconducting properties, separating the emergence of non-reciprocity from the ultimate collapse of the superconducting gap.

Rather than a single, abrupt transition, the material progresses through distinct regimes, offering a window to control and potentially stabilise the diode effect at higher temperatures. Beyond the immediate implications for low-dissipation electronics, these findings resonate with ongoing efforts to understand unconventional superconductivity in complex materials like cuprates and nickelates.

Acknowledging limitations is vital; the theoretical model relies on specific assumptions about interlayer coupling and disorder, and experimental verification across a wider range of materials is needed. The focus here is on the fundamental physics governing the diode effect, rather than device optimisation. The magnitude of the observed asymmetry remains modest, and scaling this up to practical levels presents a significant hurdle.

The field is poised for a period of intense exploration. Future work will likely focus on engineering materials with enhanced interlayer coupling and reduced disorder, potentially through advanced layering techniques or novel substrate designs. A deeper understanding of the interaction between superconductivity, non-reciprocity, and topological effects could unlock entirely new device architectures, moving beyond simple diodes towards more complex superconducting circuits. The insights gained from bilayer systems may inform the design of similar asymmetric effects in other two-dimensional materials, broadening the scope of this exciting area of research.