The discovery of graphene – a material made of a single layer of carbon atoms – 15 years ago was the first step in what has become an ongoing revolution. Using such two-dimensional layers of carbon or other compounds, materials can now be precisely engineered for particular properties in ways that had not previously been possible. Around two years ago, scientists at the Massachusetts Institute of Technology (MIT) added yet another twist – literally. They created a material made of two layers of graphene in which the top layer was slightly askew – twisted at a “magic angle” of a tad over one degree. A single layer of graphene generally behaves as a semimetal, but the magic twist turns the two graphene layers into a superconductor, in which electrons can carry electric current with no loss of energy. This superconductor somewhat resembles a completely different group of materials – so-called high-temperature superconductors – that have subject of intense research for decades but are still not fully understood.
Researchers at the Weizmann Institute of Science recently teamed up with the magic-angle group at MIT to uncover the physics of this interesting twist. Along the way, they identified a new kind of disorder – a discovery that could advance the emerging field of “twistronics.”
PhD student Aviram Uri and Dr. Sameer Grover, who led the research in the group of Prof. Eli Zeldov of the Weizmann’s Condensed Matter Physics Department, together with Yuan Cao and colleagues from the group of Prof. Pablo Jarillo-Herrero at MIT, measured the flow of electrons in magic-angle graphene using the scanning SQUID-on-tip microscope developed in Zeldov’s lab. An ultra-sensitive magnetometer with nanoscale resolution, the SQUID-on-tip is perfect for this purpose, explains Aviram. It visualizes, in great detail, what happens on the level of a single atomic, super-lattice period that is induced by the two rotated layers. The double layers of graphene-with-a-twist devices were prepared for the experiment at MIT and sent to Zeldov’s lab.
The first thing the researchers noted in their measurements was that the electrons followed “preferred” narrow paths through the material. These paths resembled quantum “edge states” that Zeldov and his team had identified in their previous experiments in graphene; but as opposed to those experiments, where the edge states were actually on the edges, here they were running right through the middle. How and why did these strange edge states form?
The solution to this puzzle, says Zeldov, is that these currents still flow along edges, but in this case the edges are the boundaries of patches within the material, each made up of different twist angles. The researchers found that even if one aims for a specific twist-angle when fabricating the device, there will be random strains and stresses so that the twist angle varies throughout -- creating a complex structure rather than a uniform one. By tracing the exact positions of the edge states, the researchers were in fact able to construct spatial maps of the local twist angle with unprecedented resolution and accuracy. These new maps revealed an intricate landscape consisting of valleys, peaks and saddle points, and a network of sharp jumps.
“Close to the magic angle, the electronic properties of the material depend strongly on the exact twist angle. That means that regions with different twist angles should really be thought of as different materials that are somehow attached together,” explains Aviram. This new perspective has far reaching implications. The researchers in Zeldov’s group showed that gradients in the twist angle lead to the formation of strong internal electric fields that do not behave as would be expected, given the metallic nature of the material. Moreover, these fields can be tuned and amplified significantly simply by changing the density of the electrons. Unlike the electric fields produced by the more familiar “charge disorder,” these electric fields reflect a fundamentally new type of disorder – “twist-angle disorder” – a phenomenon that affects the very properties of its electrons, causing them to alter their mass as they traverse the different regions of the material.
Qantum Hall edge states surprisingly appear in the bulk of magic angle graphene rather than along the edges of the device (black outline). Each edge state consists of a pair of red and blue colors indicating counterpropagating persistent currents. A scanning nanoSQUID-on-tip was used to directly image the currents through their magnetic field imprint.
The nature of this new kind of disorder gave the researchers some clues as to how edge states form in the interior of the sample. “You can think of the twisted material as a series of egg cartons with different periodicities placed side by side,” says Aviram. “The edge states run in the narrow areas that separate those ‘cartons’ – this is where intense in-plane electric fields exist, pointing from one egg carton to the next.”