Coherent Electronic Lensing in Proximitized Graphene

In the world of tiny electronics, scientists are learning to treat electrons not just as a flow of electricity, but as waves that can be guided, focused, and made to interfere with one another, much like light passing through a lens. This field, known as electron quantum optics, relies on materials where electrons can travel long distances without bumping into impurities, allowing their wave-like nature to remain intact. One of the most promising materials for this is graphene, a sheet of carbon atoms so thin it is essentially two-dimensional. Because of its unique structure, electrons in graphene move in a way that allows researchers to create electrical circuits that mimic optical devices, such as mirrors and lenses, but for electric current. Understanding how to control these electron waves is crucial for building the next generation of ultra-fast, low-power computers and sensors that rely on the delicate interference of quantum states.

A team of researchers has now demonstrated a new way to manipulate these electron waves inside a superconducting device, turning a simple probe into a tunable lens. Working with a special type of electronic junction made from graphene sandwiched between superconducting metal leads, they used a technique called Scanning Gate Microscopy. In this setup, a very sharp, electrically charged needle is moved slowly over the surface of the device without touching it. As the needle hovers, its electric field acts like a local gate, gently pushing and pulling on the electrons passing underneath. By carefully mapping how the electrical current changes as the needle moves, the scientists discovered that the tip does more than just shift the overall energy of the electrons; it actively bends their paths, focusing them like a lens to create distinct patterns of interference.

The device they studied is a ballistic graphene Josephson junction, a component where electrons travel freely between two superconducting contacts. Inside this junction, the researchers had created a specific region where the electrical charge of the electrons was reversed, forming a cavity that traps the waves. When electrons bounce back and forth between the boundaries of this cavity, they create a standing wave pattern, similar to the ripples seen when water waves reflect off a wall. The researchers wanted to see how this pattern would change if they disturbed the electrons locally with their scanning needle. They measured two things: the ability of the device to conduct electricity in a normal state, and the maximum current it could carry while remaining superconducting.

What they found was a series of beautiful, circular rings in their data maps. These rings appeared whenever the needle was moved across the junction, and they showed up in both the normal conductance and the superconducting current. At first glance, one might assume the needle was simply acting like a second gate, changing the overall density of electrons in the entire cavity. If that were the only effect, the interference patterns would simply shift smoothly as the needle moved. However, the data showed something more complex. The researchers observed that the needle was also creating a local distortion in the path of the electrons. This distortion acted as a coherent lens, altering the phase, or the timing, of the electron waves as they traveled. This lensing effect caused the interference fringes to oscillate in a specific way that could not be explained by a simple global shift in electron density.

To confirm this, the team built a mathematical model that treated the needle's influence as a combination of a broad, global effect and a sharp, local perturbation. The model successfully reproduced the circular fringe patterns seen in the experiments, proving that the local lensing was the dominant mechanism. The researchers explicitly ruled out the idea that the needle was changing the physical size of the cavity or the length of the path the electrons traveled. Instead, the evidence pointed to the needle modifying the quantum phase accumulated along the electron trajectories. This means the needle was effectively retuning the interference conditions for the waves, shifting them from constructive interference, where they reinforce each other, to destructive interference, where they cancel out.

Remarkably, this lensing mechanism worked just as well when the device was in its superconducting state. In this regime, the current is carried by pairs of electrons that have formed a special quantum bond. The researchers found that the needle could disrupt the delicate balance required for these pairs to flow without resistance. By shifting the phase of the electron waves, the tip could drive the system out of resonance, effectively turning the supercurrent on and off in specific locations. This demonstrated that the same principle of coherent lensing governs both normal electron transport and superconducting transport in these devices.

The study establishes that a scanning probe can serve as a highly precise, tunable lens for controlling quantum interference in graphene. By moving the tip, researchers can now actively steer electron waves and manipulate the conditions under which they interfere, all without altering the physical structure of the device. This capability opens new avenues for exploring how quantum coherence behaves in complex environments and suggests that future electronic devices could be dynamically reconfigured using local electric fields. The work confirms that the interplay between superconductivity and electron optics in graphene is rich with phenomena that can be harnessed for advanced control of quantum states, offering a powerful tool for the emerging field of electron quantum optics.