Magic-angle bilayer graphene enters a new phase

In 2018 Pablo Jarillo-Herrero of MIT and his colleagues demonstrated superconductivity in magic-angle bilayer graphene (see Physics Today, May 2018, page 15 ). A single layer of graphene is a two-dimensional sheet of carbon atoms and on its own is not superconducting. But two sheets (blue and black in the figure) vertically stacked at just the right angle θ —about 1.1°—with respect to each other have a superconducting transition around 1.7 K. The magic lies in the quasiperiodic structure, or moiré lattice, that forms at a larger length scale than the underlying graphene lattices, as seen in the figure. Provided the temperature is low enough, the resulting superconducting state can be summoned in and out of existence by changing the angle between the sheets of graphene or the charge carrier density with an applied voltage. Beyond that tunability, magic-angle graphene’s superconductivity is interesting because its relationship of temperature to carrier density resembles that of high-T_c cuprates.

Now Dmitri Efetov of the Institute of Photonic Sciences in Barcelona, Spain, and his colleagues have replicated Jarillo-Herrero’s results and discovered even more states in magic-angle graphene. By preparing a high-quality device, Efetov’s team could measure the electronic phases more accurately and resolve previously hidden electronic states.

To realize the magic angle, the researchers use an established technique: They take one sheet of graphene and tear it in two. They then rotate one of the pieces just past the magic angle, by about 1.2°, and stack it on top of the other. In most electrical devices, the final step is annealing to clean the sample and get rid of any air bubbles between the layers. But in magic-angle graphene, with the layers misaligned by such a small angle, heating the sample snaps the graphene layers back into alignment. Instead of annealing, Efetov and colleagues rolled the top layer down gradually, starting from one edge, rather than dropping the second layer directly down onto the first. That method squeezes out any air bubbles as they form. The result is a relative angle that varies by only 0.02° over a 10 µm device, a record for magic-angle graphene. The fabrication overall is tricky; in three months of trying, just 2 of the 30 devices worked.

The group measured the electrical resistance over a wide range of electron or hole densities—depending on whether the applied voltage was negative or positive. They saw the same superconducting state as Jarillo-Herrero, when the magic-angle graphene had a hole density of about 2 × 10¹² cm⁻², plus three new superconducting states at electron and hole densities as low as 0.5 × 10¹² cm⁻². For the original superconducting state, Efetov and his colleagues found a higher transition temperature, 3 K, than previously reported—perhaps due to their improved sample quality. The three new superconducting states had much lower transition temperatures in the hundreds of millikelvin.

At charge carrier densities between superconducting regimes, magic-angle graphene showed resistance peaks from correlated electron or hole states, which are described by collective rather than individual charge carrier behavior. Three of the correlated states were insulating, and three of them seemed semimetallic. Two of the noninsulating states were also topologically nontrivial with Chern numbers of 1 and 2. (For more on Chern numbers, see the article by Joseph Avron, Daniel Osadchy, and Ruedi Seiler, Physics Today, August 2003, page 38 .) The correlated states occurred when there were an integer number of electrons or holes for each moiré unit cell, the larger hexagons in the figure.

The states are manifestations of electron–electron interactions, as are other quantum phases of matter including some types of superconductivity. But the mechanism behind graphene’s superconductivity is still unknown. Now, though, theorists have plenty of data to work with. (X. Lu et al., Nature 574, 653, 2019 ; thumbnail image credit: ICFO/F. Vialla.)