For years many graphene researchers pursued superconductivity. In 2018 Pablo Jarillo-Herrero of MIT and his colleagues found it in so-called magic-angle bilayer graphene (see May 2018, page 15 ). A single layer of graphene, a two-dimensional sheet of carbon atoms, is not superconducting on its own. But two sheets (blue and black in figure) vertically stacked at just the right, “magic” angle—about 1.1° with respect to each other—have a superconducting transition around 1.7 K.

Now Dmitri Efetov of the Institute of Photonic Sciences in Barcelona, Spain, and his colleagues have replicated Jarillo-Herrero’s results and discovered a rich landscape of competing states in magic-angle graphene.By preparing a more homogenous device, Efetov’s team could establish and resolve previously hidden electronic states.

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Researchers long suspected graphene could have correlated states, described by collective rather than individual charge-carrier behavior. Those states, such as superconducting and Mott insulating states, are likely to occur in materials with many electrons sharing the same energy. Such conditions occur in flat regions of the band structure—around a saddle point, for instance. Monolayer graphene has a saddle point in its band structure, but it’s several electron volts higher in energy than the Fermi level, the highest occupied state of the material. Raising the Fermi level up to the saddle point isn’t feasible with an applied voltage alone. In his graduate work from 2007 to 2014 with Philip Kim, then at Columbia University and now at Harvard University, Efetov tried electrolytic gates, and other groups investigated intercalation to reach higher levels of charge-carrier doping. But none quite reached the saddle point.

2 Proc. Natl. Acad. Sci. USA 108, 12233 (2011). 2. R. Bistritzer, A. H. MacDonald,, 12233 (2011). https://doi.org/10.1073/pnas.1108174108 1 A different route to correlated behaviorwas proposed by Rafi Bistritzer and Allan MacDonald at the University of Texas at Austin back in 2011. Two layers of graphene at different relative angles form a quasiperiodic structure, or moiré lattice, at a larger length scale than graphene’s lattice constant—see the larger hexagons in figure, in which the graphene sheets nearly align at their centers and increasingly misalign toward their edges. The periodicity of the moiré lattice tunes the band structure from that of independent monolayers for large angles to that of normal bilayer graphene, which is also not superconducting, when the layers are aligned.

For two layers of graphene misaligned by 1.05°, the largest of a series of magic angles, Bistritzer and MacDonald calculated the emergence of a flat horizontal band, which varies by less than 10 meV as a function of momentum. More importantly, the flat band was at the Fermi level. In effect, the creation of a moiré lattice in bilayer graphene drags the high-energy saddle point from monolayer down to an accessible energy.

Jarillo-Herrero and colleagues assembled twisted bilayer graphene devices with relative angles near 1.1°. They first observed insulating behavior below 4 K. Although the density of states doesn’t have a gap, the strong interaction between charge carriers keeps them from moving. At even lower temperatures, increasing or decreasing the number of charge carriers leads to superconducting states. Those states can be summoned in and out of existence by changing either the angle between the graphene sheets during assembly or the charge-carrier density with an applied voltage.

2 T c cuprates. Magic-angle graphene could serve as a convenient platform for studying unconventional superconductivity. Beyond that tunability, magic-angle graphene’s superconductivity is interesting because the transition temperature’s relationship with the carrier density—the so-called superconducting dome indicated by orange dashed lines in figure—resembles that of high-cuprates. Magic-angle graphene could serve as a convenient platform for studying unconventional superconductivity.