Multiterminal Quasiballistic Josephson Effect in Monocrystalline Gold

In the world of electricity, most materials act like a crowded hallway where people bump into walls and each other, slowing their progress. This is how ordinary metals conduct current: a chaotic, diffusive flow. Superconductors, however, are different. In these special materials, electrons pair up and move in perfect unison, a state that allows them to carry electricity without any resistance at all. When two superconductors are separated by a thin barrier of normal metal, a remarkable phenomenon occurs: the supercurrent can "tunnel" across the gap, linking the two sides together. This is known as the Josephson effect. For decades, scientists have studied this effect in simple pairs, but a new frontier has opened up. Researchers are now asking what happens when you connect not just two, but many superconducting leads to a single, shared piece of metal. In this complex arrangement, the behavior of the current between any two points depends on the entire network, creating a system where the whole is greater than the sum of its parts.

A team of physicists has now brought this complex idea to life using a single crystal of gold. They built a flat, planar device where a tiny, high-purity flake of gold, only 80 nanometers thick, serves as the bridge between eight separate aluminum electrodes. The gold crystal is special because it is a perfect, single piece of matter, allowing electrons to travel through it with very few collisions. This is known as the "quasi-ballistic" regime, a state where electrons move almost as freely as light, rather than stumbling through a crowd. The researchers deposited the aluminum leads on top of the gold, creating a grid of connections. They then measured how much supercurrent could flow between different pairs of these leads as they changed the temperature and applied magnetic fields.

The results were surprising and defied the standard rules that govern simpler systems. In a typical setup, the ability of a supercurrent to cross a gap drops steadily and predictably as the distance between the leads increases. Here, the researchers found no such simple pattern. They measured four different junctions with varying lengths, ranging from 94 nanometers to over a micron. Instead of the current fading away with distance, the middle junctions carried a stronger current than the ones at the ends. This non-monotonic behavior, where the middle links are stronger than the outer ones despite being longer, proved that the junctions were not acting independently. The supercurrent flowing between any two specific electrodes was being influenced by the presence and phase of all the other electrodes in the array. The entire gold crystal was acting as a single, unified quantum object, connecting every lead to every other lead simultaneously.

To confirm this was not just a fluke or a manufacturing error, the team performed a crucial control experiment. They built identical devices using ordinary, disordered gold where electrons move in a chaotic, diffusive manner. In those standard samples, the current behaved exactly as expected: it was strong in the shortest junction and vanished completely in the longer ones. This stark contrast confirmed that the strange, interconnected behavior was a unique property of the high-quality, quasi-ballistic gold crystal. The researchers also developed a new theoretical model to explain what they saw. Their calculations, which accounted for the complex reflections of electrons off the surfaces of the thin gold crystal, matched the experimental data perfectly without needing to adjust any hidden variables.

The team further explored this multiterminal behavior by sending currents through the device in different combinations. They found that the resistance of one junction changed depending on the current flowing through a completely different pair of leads. If the system were just a simple chain of three separate links, the behavior would be predictable and linear. Instead, the measurements showed a complex web of interactions where the state of the whole system dictated the flow of electricity. Finally, they tested the device with magnetic fields. In a simple junction, the current usually oscillates in a pattern related to the size of that specific gap. In this gold crystal, the oscillations corresponded to the much larger area shared by all the leads, not just the small gap between two of them. This provided definitive proof that the magnetic field was sensing the entire network of connections.

This work establishes a new platform for studying how superconductivity behaves in complex, multi-terminal systems. By using a clean, single crystal of gold, the researchers have created a laboratory where the quantum phases of multiple superconducting leads can be tuned and studied together. This setup opens the door to exploring exotic states of matter, such as artificial topological materials, where the arrangement of superconducting phases mimics the behavior of particles in higher dimensions. The study demonstrates that when electrons are allowed to move freely in a clean environment, they can create a deeply interconnected quantum network, turning a simple piece of metal into a sophisticated circuit where every part is inextricably linked to every other.