Unusual quantum states in six-layer graphene offer clues to superconductivity

Band structure and phenomenology of semimetallic rhombohedral hexalayer graphene. a, Density of states at the Fermi energy versus carrier density n and interlayer potential U, from a tight-binding calculation. The spindle-shaped pink region indicates the simultaneous intersection of Fermi energy with the conduction and valence bands. Inset: schematic of the rhombohedral six-layer structure, with active sublattices highlighted in blue and red. b–d, Band structure near the K point for three U values marked in a, with line color denoting layer polarization. e, Longitudinal resistance versus n and perpendicular electric field E (pointing upward). Major features are outlined with dashed lines; BI and CI denote band and correlated insulators, respectively. Symbols mark the locations of selected quantum phases. Credit: Deng et al. (Nature Physics, 2026).

Graphene, a material consisting of a sheet of carbon atoms arranged in a honeycomb pattern, has proved promising for various technological applications. Materials in which several layers of graphene are stacked together can exhibit different advantageous properties.

Researchers at Cornell University in the U.S., the National Institute for Materials Science in Japan and the Max Planck Institute for the Structure and Dynamics of Matter in Germany investigated the properties of rhombohedral hexalayer graphene, which includes six graphene layers shifted sideways in a repeating pattern.

Their paper, published in Nature Physics, reports various quantum states in this material under different conditions.

"Our discovery was somewhat unexpected," Xiaomeng Liu, senior author of the paper, told Phys.org. "We originally set out to study twisted rhombohedral graphene, hoping to create isolated topological bands. However, in one device made by stacking two three-layer graphene sheets, the layers relaxed into alignment, forming rhombohedral six-layer graphene."

The researchers' initial measurements performed on rhombohedral six-layer graphene hinted at behavior that was not reported in earlier studies focusing on five-layer graphene. This inspired them to explore the material's phase diagram, a graph describing the states that a material undergoes in different conditions.

"We were particularly intrigued by a strongly correlated semimetallic regime, where electrons and holes coexist and interact," said Liu.

Exploring overlapping electronic bands in six-layer graphene

Liu and his colleagues first prepared material with six layers of graphene stacked following a rhombohedral pattern. This was done by separating thin flakes from graphite and then looking for this specific stacking configuration among isolated flakes.

The six-layer graphene stack was placed between insulating layers of hexagonal boron nitride, with graphite-based gates both above and below it. The researchers then collected various measurements.

First, they measured how easily electricity flowed through their six-layer graphene-based device while changing its temperature, the magnetic field applied to it and the number of charge carriers within it. They also measured the flow of electricity while they directed an electric field of varying intensity across the stack, from one side of the graphene layers to the other.

"A vanishing electrical resistance revealed superconductivity, while an anomalous Hall response provided evidence of orbital magnetism arising from electrons' orbital motion," explained Liu. "We also measured quantum oscillations, variations in resistance with magnetic field that allow us to reconstruct the Fermi surface and identify the types of charge carriers present."

Emergent Fermi surface and superconductivity. Credit: Nature Physics (2026). DOI: 10.1038/s41567-026-03443-9

The team ultimately identified various electronic states in their hexalayer graphene device, including interaction-driven insulating states, regions of the phase diagram with superconducting behavior and two different types of orbital magnetism. Two of the superconducting-like states they observed emerged specifically under conditions where electron and hole carriers coexisted, suggesting that both carrier types might contribute to their formation.

"Our main finding is the discovery of a new superconducting state and a new multiferroic orbital magnet in rhombohedral six-layer graphene," said Liu. "Both emerge in a strongly correlated semimetallic regime, where electrons and holes coexist and interact. Our results suggest that interactions between these two types of charge carriers play a central role in the formation of these unusual states."

A route toward electrically controlled quantum materials

This study highlights the potential of six-layer graphene for studying the emergence of superconductivity and magnetic behavior driven by electron interactions. Other research teams could draw inspiration from the team's findings and set out to further probe the phase diagram of rhombohedral hexalayer graphene.

Liu and his colleagues are now further investigating the multiferroic orbital magnetic state they observed in their device. Specifically, they are trying to understand how electrons and their interactions contribute to the emergence of this state on a microscopic scale.

"Our ongoing work raises the possibility that some carriers form an electron crystal while others remain in a conducting, liquid-like state," added Liu. "We are gathering further evidence to determine whether this crystal produces orbital magnetism, and whether it could realize a topological electron solid. These remain open questions that extend beyond the findings established in the present paper."

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Publication details

Jinghao Deng et al., Superconductivity and ferroelectric orbital magnetism in semimetallic rhombohedral hexalayer graphene, Nature Physics (2026). DOI: 10.1038/s41567-026-03443-9.

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