Electron vortex detected in graphene


Researchers at ETH Zurich have shown for the first time how electrons form vortices in a material at room temperature. Their experiment used an extremely high resolution quantum sensing microscope.

When a simple 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. While moving, the 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 that can be felt, for example, by touching an incandescent light bulb.

While collisions with lattice impurities occur frequently, collisions between electrons are very rare. However, the situation changes when graphene, a 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 the dominant role. In this case, the electrons behave more like a viscous fluid. Therefore, well-known flow phenomena such as vortices should occur in the graphene layer.

Reporting in the scientific journal Science, researchers at ETH Zurich in Christian Degen's group have now managed to directly detect electron vortices in graphene for the first time using a high-resolution magnetic field sensor.

Highly Sensitive Quantum Sensing Microscope

The vortices were formed into tiny spherical disks that Degen and his colleagues attached to a conducting graphene strip just one micrometer wide during the fabrication process. The discs had diameters varying between 1.2 and 3 micrometres. Theoretical calculations suggested that electron vortices should form in smaller disks, but not in larger disks.

To make the vortices visible, the researchers measured tiny magnetic fields generated by electrons flowing inside the graphene. For this purpose, they used a quantum magnetic field sensor with a so-called nitrogen-vacancy (NV) center embedded in the tip of a diamond needle. Being an atomic defect, the NV center behaves like a quantum object whose energy level depends on the external magnetic field. Using laser beams and microwave pulses, the quantum state of the center can be tailored in such a way that it is maximally sensitive to the magnetic field. By reading quantum states with lasers, researchers can determine the strength of those fields very precisely.

“Due to the small dimensions of the diamond needle and the small distance from the graphene layer – only around 70 nanometers – we were able to make the electron streams visible with a resolution of less than a hundred nanometers,” says former Marius Palm. PhD student in the Dagen group. This resolution is sufficient to see the vortices.

reverse flow direction

In their measurements, the researchers observed a typical signature of vortices expected in small disks: a reversal of flow direction. While in normal (extended) electron transport, electrons in the strip and disk flow in the same direction, in the case of the vortex, the direction of flow inside the disk is reversed. As predicted by calculations, no vortices could be observed in the larger disk.

“Thanks to our extremely sensitive sensor and high spatial resolution, we did not even need to cool the graphene and were able to conduct the experiment at room temperature,” says Palm. Furthermore, he and his colleagues detected not only electron vortices, but also vortices produced by hole carriers. By applying an electric voltage from the bottom of the graphene, they changed the number of free electrons in such a way that the current flow is no longer carried by electrons, but by missing electrons, also called holes. Only at the charge neutrality point, where there is a small and balanced concentration of both electrons and holes, did the vortices disappear completely.

“At this point, detecting electron vortices is basic research, and there are still a lot of open questions,” says Palm. For example, researchers still need to figure out how the collisions of electrons with graphene's boundaries affect the flow patterns, and what effects are happening even in smaller structures. The new detection method used by the ETH researchers also allows a closer look at many other exotic electron transport effects in mesoscopic structures – phenomena that occur on length scales ranging from several tens of nanometers to a few micrometers.


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