Electron vortices in graphene were detected for the first time

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Using a magnetic field sensor (red arrow) inside a diamond needle, the ETH scientists imaged the electron vortices in the graphene layer (blue). Credit: Chaoxin Ding

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Using a magnetic field sensor (red arrow) inside a diamond needle, the ETH scientists imaged the electron vortices in the graphene layer (blue). Credit: Chaoxin Ding

When an ordinary electrical conductor—such as a metal wire—is connected to a battery, the electrons in the conductor are accelerated by the electric field created by the battery. When moving, electrons often collide with impurity atoms or vacancies in the crystal lattice of the wire and convert part of their kinetic energy into lattice vibrations. The energy lost in this process is converted into heat, which can be felt, for example, by touching a light bulb.

While collisions with lattice impurities occur frequently, collisions between electrons are much rarer. However, the situation changes when graphene, a single layer of carbon atoms arranged in a honeycomb lattice, is used instead of the usual iron or copper wire.

In graphene, impurity collisions are rare and collisions between electrons play a major role. In this case, the electrons behave more like a viscous liquid. Therefore, well-known flow phenomena such as vortices should occur in the graphene layer.

Journal reporting Sciencescientists from ETH Zurich in Christian Degen’s group have now succeeded for the first time in directly detecting electron vortices in graphene using a high-resolution magnetic field sensor.

A highly sensitive quantum scanning microscope

The vortices formed in small circular discs that Degen and his collaborators attached to a conductive graphene strip just one micrometer wide during the manufacturing process. The discs varied in diameter between 1.2 and 3 micrometers. Theoretical calculations suggested that electron vortices should form in smaller but not in larger disks.

To make the vortices visible, the researchers measured small magnetic fields created by electrons flowing inside the graphene. For this purpose, they used a quantum magnetic field sensor consisting of a so-called nitrogen vacancy (NV) center embedded in the tip of a diamond needle.

As an atomic defect, the NV center behaves as a quantum object whose energy levels depend on the external magnetic field. Using laser beams and microwave pulses, the quantum states of the center can be prepared so that they are maximally sensitive to magnetic fields. By reading the quantum states with a laser, scientists could determine the strength of these fields very precisely.

“Due to the small dimensions of the diamond needle and the small distance from the graphene layer – just 70 nanometers – we were able to visualize the electron currents with a resolution of less than a hundred nanometers,” says Marius Palm, a former Ph.D. student in Degen’s group. This resolution is sufficient to display vortices.

Reverse flow direction

In their measurements, the scientists observed a characteristic feature of vortices expected in smaller disks: a reversal of flow direction. While in normal (diffusive) electron transport the electrons flow in the same direction in the belt and the disk, in the case of a vortex the direction of flow inside the disk is reversed. As the calculations predicted, no eddies could be observed in the larger disks.

“Thanks to our extremely sensitive sensor and high spatial resolution, we didn’t even need to cool the graphene and were able to perform experiments at room temperature,” says Palm. Moreover, he and his colleagues detected not only electron vortices, but also vortices formed by hole carriers.

By applying an electric voltage from below the graphene, they changed the number of free electrons so that the current flow was no longer carried by electrons, but by missing electrons, also called holes. Only at the point of charge neutrality, where there is a small and even concentration of both electrons and holes, the vortices have completely disappeared.

“At this point, the detection of electron vortices is basic research, and there are still a lot of open questions,” says Palm. For example, researchers still need to learn how electron collisions with graphene boundaries affect the flow pattern and what effects occur in even smaller structures.

The new detection method used by the ETH researchers also enables a closer look at many other exotic effects of electron transport in mesoscopic structures – phenomena that occur on length scales from a few tens of nanometers to a few micrometers.

More information:
Marius L. Palm et al, Observation of simultaneous whirlpools in graphene at room temperature, Science (2024). DOI: 10.1126/science.adj2167

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