Untwisted trilayer graphene hosts superconductivity and magnetism
Electrons typically propagate without interacting in graphene, a single layer of carbon atoms arranged in a honeycomb lattice. But when three sheets of graphene are stacked on top of one another so that their lattices are aligned but offset — forming rhombohedral trilayer graphene — an electric field can be used to induce interactions between the electrons. In two papers in Nature , Zhou et al . report that these interactions give rise to ferromagnetism 1 , the type of magnetism found in iron magnets, and superconductivity 2 (zero electrical resistance). These states have already been observed in other trilayer configurations, in which the graphene sheets are slightly rotated out of alignment with each other or with a substrate, but rhombohedral trilayer graphene is more structurally stable than these materials. Read the paper: Half- and quarter-metals in rhombohedral trilayer graphene The crystal structure of rhombohedral trilayer graphene leads to a particular relationship between the kinetic energy and momentum of each electron, known as the material’s band structure. Applying an electric field modifies this band structure such that a large number of electrons with different values of momentum can populate a narrow range of energies 3 , and this strengthens the interaction between electrons. Zhou et al . discovered that their layered graphene exhibited multiple electronic ground states by measuring its electrical resistance and its electronic compressibility, which is the change in the energy of a system when an extra electron is added. Typically, the compressibility is positive because the energy of the system increases with each electron added, much as the level of water in a cup rises as more is poured in. However, when the authors varied the electric field and the electron density, they detected multiple regions of positive compressibility separated by boundaries of negative compressibility, which usually indicates a phase transition between different electronic ground states 4 . Imagine that our cup can expand if the water level reaches a certain height — immediately after the expansion, the water level will go down, even as more water is added. Read the paper: Superconductivity in rhombohedral trilayer graphene To understand more about these phases, Zhou et al. studied the system’s response to in-plane and out-of-plane magnetic fields. An electron has an intrinsic magnetic moment, which points either up or down depending on its angular momentum (also known as spin). When electrons do not interact, it is energetically favourable to have equal numbers with spin up and spin down, resulting in no net magnetic moment. Electrons can also be characterized by two minima in their band structure, known as their valley degrees of freedom, taking values K and K′. Together, these four states — (up, K), (up, K′), (down, K) and (down, K′) — define the isospin of an electron. When the density of charge carriers (electrons and their positive counterparts) is high, all four isospin states are equally represented, yielding a symmetric phase with no net magnetic moment (Fig. 1). But in rhombohedral trilayer graphene, Zhou et al. 1 found two distinct ferromagnetic phases at intermediate and low carrier densities. At the intermediate density, they observed a half-metallic phase, in which all the electron spins were pointing the same way, but the valley variables were evenly distributed between K and K′. At the low density, both spins and valleys took a single value, and the authors dubbed this a quarter-metallic state, referring to the spin–valley combination taking one state of four possibilities. These phases differ from those in most conventional ferromagnets, in which both types of spin are present, but in different proportions. Figure 1 Phases in rhombohedral trilayer graphene. Zhou et al. 1 , 2 studied rhombohedral trilayer graphene, in which three sheets of graphene are layered such that their lattices are offset (not shown). When the density of charge carriers (electrons and their positive counterparts) is high, this material exhibits a symmetric phase, in which electrons are equally likely to have their spins (angular momenta) pointing up or down, and energy minima known as valley degrees of freedom take values K (yellow) and K′ (blue), which are equally probable. At intermediate carrier density, the spin directions align and the system becomes a half-metallic ferromagnet, characterized by the type of magnetism seen in iron, but the valley variables are distributed evenly between K and K′. At low carrier density, there is a quarter-metallic phase, in which all the spins point in the same direction and valley degrees of freedom take only one value. At very low temperatures, superconducting phases (SC1 and SC2) emerge from the symmetric and half-metallic phases, respectively. These phases require a pairing between two electrons, of a form that is not yet known. Two distinct superconducting phases also emerge in Zhou and co-workers’ system: one (SC1) from the symmetric phase below a transition temperature of 100 millikelvin (mK) and one (SC2) from the half-metallic phase below a transition temperature of 20?mK. Superconductivity relies on a pairing mechanism that allows two electrons to overcome the repulsion arising from their like charges. In a conventional superconductor, this pairing occurs between electrons with opposite spins through vibrations of the crystal lattice that hosts the electrons. A magnetic field can therefore destroy superconductivity by aligning the electron spins, and breaking the pairing. Zhou et al . 2 applied an in-plane magnetic field, which couples to the electron spins, and observed that the superconductivity in SC1 disappeared at a magnetic field strength of 300 millitesla (mT). This is commensurate with the magnetic field strength required to align spins in a conventional superconductor, known as the Pauli paramagnetic limit. However, the authors found that the superconductivity in SC2 persisted to much larger values of magnetic field strength — more than 1?T — violating the Pauli paramagnetic limit by at least a factor of ten. This large field strength, together with the fact that all the spins usually point the same way in SC2, suggested a pairing between the electrons with aligned spins. Superconductivity in a graphene system survives a strong magnetic field Although SC1 and SC2 behave differently under a magnetic field, they share a few common features. For example, they are both characterized by an annular Fermi surface, which describes the momenta of electrons at a given energy. Both states also occur at parameters that are close to those at which phase transitions to more ordered states take place. On the strength of this evidence, Zhou et al . hypothesized that fluctuations in the ordered states, such as spin, might mediate a pairing mechanism, as proposed in other systems 5 . Superconductivity and magnetism have been observed previously in moiré graphene systems, in which there is rotational misalignment between layers. For example, ferromagnetism 6 and signatures of superconductivity 7 have been reported in moiré rhombohedral trilayer graphene, and the Pauli limit has also been found to be violated in another type of twisted trilayer graphene 8 . But the lattice structure of moiré systems is more complicated than that of rhombohedral trilayer graphene, making it more difficult to study. Rhombohedral trilayer graphene is also easier to obtain because it exists in nature, whereas moiré systems need to be engineered. Zhou et al . measured the electronic compressibility in moiré rhombohedral trilayer graphene and found it largely unchanged compared with the untwisted material, with the exception of extra energy gaps in the band structure introduced by the twist. The similarity between the behaviour of the ferromagnetic and superconducting states in rhombohedral trilayer graphene and moiré graphene systems might hint at a close connection between the mechanisms underlying these states. Further studies in rhombohedral graphene will be required to confirm and determine the origins of these phases. For example, measuring a type of particle scattering known as Andreev reflection 9 will provide further evidence that the spins are fully aligned in the quarter- and half-metallic phases even in the absence of a magnetic field. The simple lattice structure and reproducibility of rhombohedral trilayer graphene could help theoretical and experimental studies aimed at revealing the nature of the phases identified by Zhou and colleagues — and might offer insights into other moiré graphene systems. .