• Physics 18, 143
An unprecedented combination of superconducting states has been found in multilayer graphene with a rhombohedral structure.
Crystals made of a few layers of graphene are even more intriguing than the single-layer original. One recipe for making them is to shift each newly stacked layer sideways by a third of the width of the unit cell. This so-called ABC stacking repeats itself every three layers in a pattern that resembles a rhombohedron. Superconductivity was discovered in rhombohedral graphene four years ago [1]. Now Long Ju of MIT and his collaborators have found two new superconducting states in the material [2]. Each state exhibits both chirality and magnetism—a combination of properties that has not been seen before in a superconductor. The results suggest that researchers could be getting closer to so-called topological superconductivity, a type of electronic state that might prove useful in future, less-error-prone quantum computers. “[Rhombohedral graphene] is probably the best candidate for a topological superconductor discovered,” says physicist Andrea Young of the University of California, Santa Barbara, who was not involved in the study.
The interest in rhombohedral graphene stems from the shape of its bands. Whereas single-layer graphene’s conduction and valence bands meet sharply at a point, ABC stacking splits the points and flattens the bands. Electrons that occupy a flat band share the same low energy regardless of their momentum. Interactions among these sluggish electrons are relatively stronger than those for electrons occupying the sharper bands characteristic of semiconductors. In rhombohedral graphene, the combination of flat bands, crystal symmetries, and electron-occupation rules creates an undulating, spin-dependent landscape where various collective electronic phenomena can arise. Experimenters have two main ways to shepherd the electrons within this landscape. First, they can inject additional electrons into the crystal, which boosts the density and pushes electrons into higher-energy locations. Second, researchers can apply a voltage across the crystal, raising and flattening the landscape itself.
Ju and his collaborators followed that two-pronged approach, which has already enabled them and others to discover superconductivity, ferromagnetism, and the fractional quantum anomalous Hall effect in rhombohedral graphene. The team made 4- and 5-layer samples of rhombohedral graphene and equipped them with electrodes. They measured the resistance and found that it vanished for three separate regions in the parameter space of the applied electric field and density of injected electrons. These regions—which the team labelled SC1, SC2, and SC3—had not been identified in previous studies of superconductivity in rhombohedral graphene.
To explore these new superconducting states, the researchers focused on the type of pairing of electrons in each region. Electron pairs are characterized by their total spin S and their orbital angular momentum L. As an electron pair is made up of two spin-1/2 fermions, the value of S is either 0 or 1. And because the pair’s wave function is antisymmetric, the value of L depends on S: If S = 0, L must be an even integer; if S = 1, L must be an odd integer. A particularly interesting combination is S = 1 and L = 1, as that state would be chiral. The chirality in this case is not related to a mirror symmetry (as in left-handed and right-handed structures), but instead it involves time-reversal symmetry: The direction of the orbital angular momentum changes sign when the time variable is run backward.
To determine the S and L values in the three superconducting states, Ju and his collaborators carried out a range of tests. Applying a modest perpendicular magnetic field of 0.1 tesla (T) sufficed to destroy SC3, suggesting that the electron pairs in that superconducting state have antiparallel (S = 0) pairing and that their coupling is based on the conventional Bardeen-Cooper-Schrieffer model. But SC1 and SC2 survived beyond 0.6 T. What’s more, SC1 and SC2 were also largely immune to the application of an in-plane magnetic field, suggesting that the electrons have parallel (S = 1) pairing.
It’s not possible to measure L directly, but the researchers uncovered strong evidence that L is nonzero in SC1 and SC2. For one, they observed hysteresis in the resistance of their samples as an applied magnetic field was swept back and forth between values of –0.1 and +0.1 T. Such hysteresis indicates ferromagnetism in the SC1 and SC2 states. In addition, the resistance of the neighboring metallic state exhibited a Hall effect at 0 T, that is, an anomalous Hall effect. Both ferromagnetism and the anomalous Hall effect are manifestations of electrons with nonzero orbital momentum.
The fact that SC1 and SC2 are magnetic and chiral suggests the coupling between the electrons may be different from that in more conventional superconductors. Indeed, if the coupling brings the paired electrons close enough to each other, they may form a topological superconductor state. The signature of topological superconductivity would be Majorana modes—robust collective topological states that are predicted to reside along the edges of these materials. However, the paired electrons could be too close, in which case they cannot form a topological state. From the longitudinal resistance’s dependence on a perpendicular magnetic field, Ju and his collaborators could infer the size of the electron pairs in SC1 and SC2. Of the two, SC1 is less likely to be topological than SC2, but neither is within the “too close” limit, Ju says.
Even if neither SC1 nor SC2 turn out to be topological, they are nevertheless unique. “SC1 and SC2 are phenomenologically distinct from all other superconductors, which is a remarkable thing given the long history of superconductivity,” Ju says.
–Charles Day
Charles Day is a Senior Editor for Physics Magazine.
References
- H. Zhou et al., “Superconductivity in rhombohedral trilayer graphene,” Nature 598, 434 (2021).
- T. Han et al., “Signatures of chiral superconductivity in rhombohedral graphene,” Nature 643, 654 (2025).
