Twisting two sheets of graphene together through a "magic" angle gives rise to some intriguing quantum phenomena in the resulting structure, which gives rise to a periodic "moiré" pattern. Among those phenomena are superconductivity, magnetism, and insulating behavior. As such researchers are keen to study this so-called magic angle.

Now, Shahal Ilani of the Weizmann Institute in Israel working with Pablo Jarillo-Herrero and colleagues at Massachusetts Institute of Technology, have demonstrated that the novel quantum phase of twisted graphene sheets emerges from a previously unknown high-energy parent state that undergoes symmetry breaking.

In twisted bilayer graphene, electrons in the misaligned sheets can have up or down spin as normal but also exist in valleys originating in the hexagonal lattice of the graphene. As such each site in the twisted bilayer can hold up to four electrons without breaking the Pauli exclusion principle.

If all moiré sites are full - four electrons per site - the material acts as an insulator. However, in 2018, the researchers had found that it could be an insulator at "magic" twist angle even if there are only two or three electrons per moiré site. Single particle physics cannot explain this and the scientist invoke the concept of an exotic "correlated Mott insulator" to explain it. More intriguing, however, was that with such occupancy, superconductivity arose in the magically twisted materials.

To investigate, the Weizmann team positioned a carbon nanotube single-electron transistor at the edge of a scanning probe cantilever. This allowed them to image, in real space, the electric potential produced by electrons in a material with extreme sensitivity.

"Using this tool, we could image for the first time the 'compressibility' of the electrons in this system - that is, how hard it is to squeeze additional electrons into a given point in space," says Ilani. "Roughly speaking, the compressibility of electrons reflects the phase they are in: In an insulator, electrons are incompressible, whereas in a metal they are highly compressible."

The team anticipated that this compressibility would follow the simple electron-filling pattern. However, the results were much more complicated. Instead of observing a symmetric transition from metal to insulator and back to metal, they saw a sharp, asymmetric jump in the electronic compressibility near the integer fillings. This implies that the nature of the carriers before and after the transition is different. Before the transition the carriers are heavy and afterwards they are extremely light, like Dirac electrons present in graphene.

The phase transitions and Dirac electrons are seen at temperatures well above the superconducting and correlated insulating state transition temperatures. This suggests that the observed broken symmetry state is actually the parent state from which the phenomena emerge. This might ultimately be exploited in controlling the quantum phenomena in novel twisted forms of graphene. [Zondiner, U. et al., Nature; 582, 203-208; DOI: 10.1038/s41586-020-2373-y]

David Bradley