Do superconductivity and insulating behavior in MATBG have the same physical origin? That’s a key question for researchers to address. At the microscopic level, superconductivity occurs when electrons pair, and the pairs form a single, coherent quantum state. In most simple metals, the pairing is between weakly interacting band electrons. In this picture, any tendency of the electrons to form an insulating phase would suppress superconductivity because fewer electrons would be available to pair. But there is a more exotic possibility, where superconductivity and insulating behavior are “friends.” Here, the pairing occurs between heavily interacting quasiparticles, which move in a correlated-electron environment that locally favors an insulating state. This scenario might, in some systems, like the cuprates, allow superconductivity at much higher temperatures. The idea, however, is not well understood, and there is much hope that we will learn something new and meaningful about it from MATBG.

Whether this hope will be realized in MATBG depends on the relationship between superconductivity and insulating behavior. So far, researchers have determined at least one connection, which is that the two phenomena depend mainly on the same parameter, the moiré filling factor, 𝜈 M . This parameter defines the fraction of filled states in a given band, and it can be tuned with an electronic gate. Such tuning experiments have observed that insulating states occur at most integer values of 𝜈 M , whereas superconductivity frequently occurs when 𝜈 M is close to, but not equal to, an integer. As a function of experimentally controllable parameters, like twist angle, gate voltage, and pressure, the two phenomena seem to come and go together like pencil and paper (Fig. 2). Establishing that the two phases live and die together would provide a powerful clue that they are related, whereas showing that the two states' existence is only loosely tied together may be a sign that they compete. In this “competing” world, the insulating phase would almost certainly be driven by Coulomb interactions between electrons, while superconductivity could arise mainly from conventional phonon-mediated pairing. Conventional pairing is a realistic possibility; after all, superconductivity is common in graphene-based systems with a high density of states at the Fermi level, such as intercalated graphite. What makes MATBG special in this scenario is simply that it has flat bands, which yield very high densities of states at a very low carrier density.