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When an ordinary electrical wire – such as a metal wire – is connected to a battery, the electrons in the wire are accelerated by the electric field created by the battery. As they move, the electrons often collide with impurity atoms or vacancies in the crystal lattice of the wire and convert some of their energy of motion into lattice vibrations. The energy lost in this process is converted into heat that can be felt, for example, by touching an incandescent 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 ordinary iron or copper wire.

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

Journal reporting Scienceresearchers at ETH Zurich in Christian Degen’s group were able to directly detect electron vortices in graphene for the first time using a high-resolution magnetic field sensor.

A highly sensitive quantum sensing microscope

The vortices formed in small circular discs that Degen and his colleagues had attached during the manufacturing process to a conductive graphene ribbon just one micrometer wide. The discs have different diameters between 1.2 and 3 micrometers. Theoretical calculations suggest that electron vortices should form in the smaller but not in the larger discs.

To make the vortices visible, the researchers measured the tiny magnetic fields produced by the 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 an external magnetic field. Using laser beams and microwave pulses, the quantum states of the center can be prepared in such a way that they are maximally sensitive to magnetic fields. By reading the quantum states with a laser, researchers can 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 – only about 70 nanometers – we were able to make the electron currents visible with a resolution of less than a hundred nanometers,” says Marius Palm, former Associate Ph.D. student in Degen’s group. This resolution is sufficient to see the eddies.

Reverse flow direction

In their measurements, the researchers observed a characteristic feature of vortices expected in smaller discs: a reversal of flow direction. While in normal (diffusive) electron transport, the electrons in the band and disc flow in the same direction, in the case of a vortex the direction of flow inside the disc is reversed. As predicted by the calculations, no vortices can be observed in the larger discs.

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

By applying an electrical voltage to the bottom of the graphene, they change the number of free electrons in such a way that the current flow is no longer carried by electrons, but rather by missing electrons, also called holes. Only at the point of charge neutrality, where there is a small and balanced concentration of electrons and holes, did the vortices disappear completely.

“At this point, the detection of electron vortices is basic research, and there are still many open questions,” says Palm. For example, researchers still need to understand 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 allows for 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.