Unusual superconductivity could emerge in valley-imbalanced rhombohedral graphene

27/08/2026
The emergent vortex lattice. Credit: Christos et al. (PRL, 2026).


Superconductors are materials in which electrical current flows with a resistance of zero, typically below specific temperatures. In conventional superconductors, this state of matter emerges when two electrons bind together at low temperatures, forming so-called Cooper pairs.

Yet some materials, referred to as unconventional superconductors, exhibit superconductivity under unusual conditions and cannot be explained by conventional theories. Understanding these unusual cases could lead to the development of superconductors that can operate at high enough temperatures to be used in real-world devices with less refrigeration.

Researchers at Harvard University and the University of Stuttgart theoretically demonstrated that an unusual form of graphene, known as valley-imbalanced rhombohedral tetralayer graphene, could host unconventional superconducting states.

Their paper, published in Physical Review Letters, suggests that superconductivity in this material could simultaneously condense at multiple incommensurate momenta, leading to the spontaneous formation of a superlattice of Cooper pairs.

"Our work was inspired by an experiment that showed that superconductivity can emerge out of a normal state in a specific stack of graphene layers called rhombohedral graphene, where electrons in two valleys of graphene spontaneously choose to fill one valley over the other," Mathias Scheurer, corresponding author of the paper, told Phys.org.

"This is very exciting since the two valleys of graphene are related by time-reversal symmetry and thus an imbalance between the two spontaneously breaks this symmetry. Yet this symmetry is central to superconductivity; so much so that virtually all theoretical works focusing on conventional or unconventional superconductivity begin by assuming it is not broken. As such, it was of fundamental interest to identify what the key modifications are to the theory of superconductivity if this symmetry is absent."


The superconducting order parameter. Credit: Christos et al. (PRL, 2026).


The emergence of a superconducting superlattice in graphene

Scheurer and his co-authors Maine Christos and Pietro M. Bonetti developed a theoretical framework that could be used to classify possible superconducting pairing instabilities in rhombohedral tetralayer graphene. In conventional superconductors, paired electrons typically have opposite momenta (i.e., motions), so their collective net momentum vanishes.

The team's framework also considers electron pairs with nonzero momentum. It also distinguishes between commensurate states and incommensurate states. The first are superconducting patterns compatible with the periodicity of a material's underlying crystal lattice, while the latter have a periodicity that does not match the crystal lattice.

"Some of us had previously worked on transport signatures of superconductors with valley imbalance, motivated by the fact that it stabilizes nonreciprocal critical currents, i.e., critical currents that differ in forward and reverse directions," said Scheurer.

"As such, we had already developed a good understanding of some of the basics of the interplay of valley imbalance and pairing. This study was a very natural next step for us, as it allowed us to look into it further."


The team's experimental setup. Credit: https://arxiv.org/abs/2408.15233


The researchers wanted to use their framework to shed light on whether superconductivity can coexist with broken time-reversal symmetry. To do this, they used various numerical and analytical techniques. Most notably, they looked for numerical solutions to the so-called linearized gap equation, an equation that can be used to predict what types of superconductivity are energetically favorable under specific experimental conditions.

"Because the precise degree of symmetry breaking in the experiment was unknown, we chose to study a wide range of scenarios of initial conditions and interactions to account for as many experimental scenarios as possible," explained Christos.

"Excitingly, we found that for the initial conditions most likely to be realized in rhombohedral graphene, the superconductor carried a special type of topology that we analytically showed is determined by the underlying interactions in the system. Beyond this, we used a calculation of free energy to show that the superconducting state could possibly have even more exotic features and may also spontaneously break translational symmetry."

Prompting new experiments with rhombohedral graphene

Chirality is an important physical concept indicating that something (e.g., a human hand) cannot be transformed into its mirror image simply by rotating it. Superconductors can also be chiral, in the sense that the movement of electrons and how superconductivity is organized give rise to distinct regions (i.e., valleys) with their own chirality.

"One of the questions we addressed is the relation between the chirality of the favored valley in rhombohedral graphene out of which superconductivity emerges and the chirality of the superconductor," said Bonetti. "A well-known feature of superconductors is that they develop vortices—like whirlwinds in the superconductor—when a sufficiently strong magnetic field is applied. They typically arrange in a spatially regular fashion, i.e., develop a vortex lattice."

The team's theoretical framework suggests that superconductors emerging out of a valley-imbalanced normal state can spontaneously develop a so-called vortex lattice, even in the absence of an external magnetic field. Experimental physicists could soon set out to test this prediction in the lab and search for the spatial superlattice pattern described by the authors.

"There are many other interesting aspects to explore about superconductivity in valley-imbalanced rhombohedral graphene," added Scheurer.

"One, which we have already started exploring, is unique features associated with the interaction with light. Another interesting direction is to analyze inhomogeneities, which we have also started to investigate for the case of random disorder, but intentional inhomogeneities, like tunnel junctions, could also turn out to be very fruitful."

Source: https://tinyurl.com/s7bwnpc2  via Phys.org