🔬 mesoscale physics

Superconductivity and spin canting in spin-orbit proximitized rhombohedral trilayer graphene

By introducing spin-orbit coupling via substrate proximity in rhombohedral trilayer graphene, researchers demonstrated a tripling of the superconducting critical temperature driven by a quantitative change in spin-canting angles rather than a change in ground state symmetry, suggesting that fluctuations in this magnetic order facilitate the pairing interaction.

Original authors: Caitlin L. Patterson, Owen I. Sheekey, Trevor B. Arp, Ludwig F. W. Holleis, Jin Ming Koh, Youngjoon Choi, Tian Xie, Siyuan Xu, Evgeny Redekop, Grigory Babikyan, Haoxin Zhou, Xiang Cheng, Takashi Tanig

Published 2026-08-05

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CC BY 4.0

Original authors: Caitlin L. Patterson, Owen I. Sheekey, Trevor B. Arp, Ludwig F. W. Holleis, Jin Ming Koh, Youngjoon Choi, Tian Xie, Siyuan Xu, Evgeny Redekop, Grigory Babikyan, Haoxin Zhou, Xiang Cheng, Takashi Taniguchi, Kenji Watanabe, Chenhao Jin, Etienne Lantagne-Hurtubise, Jason Alicea, Andrea F. Young

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where electricity flows without any resistance, like a ghost gliding through a wall without ever bumping into a single brick. This is the magic of superconductivity, a phenomenon that could revolutionize everything from power grids to quantum computers. But for scientists, the real puzzle isn't just that it happens, but why. In recent years, researchers have been playing with ultra-thin sheets of carbon (graphene) and other materials, stacking them like pancakes to create "flat-band" systems. These are special playgrounds where electrons get stuck together, behaving like a crowded dance floor where everyone moves in sync. Sometimes, this sync leads to magnetism (like tiny compass needles pointing the same way), and sometimes, it leads to superconductivity. The big question hanging over the field is: Do these magnetic dances fight the superconductivity, or do they actually help the electrons pair up and dance together?

Enter the scientists at this paper, who decided to test this by adding a secret ingredient: spin-orbit coupling. Think of this as a "magnetic wind" that blows on the electrons, forcing them to twist and turn in specific ways depending on how they move. They took a stack of three graphene sheets (rhombohedral trilayer graphene) and placed it right next to a material called tungsten diselenide (WSe2). This proximity acts like a magnet, injecting that "magnetic wind" into the graphene. Their goal was to see if this wind could turn up the volume on superconductivity and, if so, what kind of dance the electrons were doing when they decided to become superconductors.

Here is what they found: The "magnetic wind" worked like a charm, but not in the way everyone expected. When they turned up the spin-orbit coupling, they didn't just get a little more superconductivity; they unlocked entirely new pockets of superconductivity for both electron and hole doping. The most exciting part? The temperature at which this superconductivity happened jumped to about 300 millikelvin (mK), which is three times hotter than what they saw in graphene without the extra magnetic wind.

But the real story is about the dance moves. The researchers used a tiny, super-sensitive magnetic camera (a nanoSQUID) to peek at the electrons' spins. They discovered that the superconductivity didn't appear in a state where the spins were perfectly locked in a rigid, frozen pattern. Instead, it appeared right in the middle of a transition where the spins were "canting"—a fancy word for tilting or leaning over. Imagine a group of soldiers who used to stand perfectly straight (locked spins) suddenly starting to lean at a slight angle. The paper suggests that this leaning, or "spin canting," is the secret sauce. The electrons aren't just sitting still; they are in a state of flux, leaning back and forth, and it is this specific kind of wobble that helps them pair up to become superconductors.

The team used computer simulations (Hartree-Fock calculations) to back this up, showing that the competition between the "magnetic wind" (spin-orbit coupling) and the natural desire of electrons to align (Hund's interaction) creates this perfect leaning angle. They ruled out the idea that the superconductivity was caused by a completely new, strange type of magnetic order; instead, it's a quantitative change in how much the spins are leaning. In short, the paper suggests that to get the best superconductivity, you don't need the spins to be perfectly rigid or perfectly chaotic; you need them to be just right in that sweet spot of a gentle, continuous tilt. This discovery helps us understand that the secret to making better superconductors might lie in tuning these subtle magnetic angles, opening a new door for designing materials that could one day power our world without losing a single drop of energy.

Technical Summary: Superconductivity and Spin Canting in Spin-Orbit Proximitized Rhombohedral Trilayer Graphene

Problem Statement
Two-dimensional flat-band systems, including twisted graphene multilayers and transition metal dichalcogenide (TMD) heterostructures, exhibit complex phase diagrams featuring intertwined magnetic and superconducting orders. A central unresolved question is whether magnetic ordering competes with or facilitates superconductivity. Recent studies in Bernal bilayer graphene demonstrated that enhancing spin-orbit coupling (SOC) via proximity to a WSe $_2$ substrate significantly increases the critical temperature ( $T_c$ ) and the domain of superconductivity. However, the microscopic mechanism driving this enhancement remains unclear. Specifically, it is unknown whether the enhancement arises from a qualitative change in ground state symmetry or a quantitative modification of existing magnetic orders.

Methodology
The authors investigated rhombohedral trilayer graphene (RTG) devices encapsulated between hexagonal boron nitride (hBN) and WSe $_2$ flakes to induce strong Ising spin-orbit coupling ( $\lambda \approx 1.5$ meV). The study employed a multi-modal experimental approach:

Transport Measurements: Longitudinal resistivity ( $R_{xx}$ ) was measured as a function of carrier density ( $n_e$ ) and perpendicular displacement field ( $D$ ) to map superconducting pockets and phase boundaries.
Thermodynamic Measurements: Inverse compressibility ( $\kappa = \partial\mu/\partial n$ ) was measured to identify phase transitions and Fermi surface topology.
Local Magnetometry: NanoSQUID-on-tip sensors were used to image local fringe magnetic fields, probing the spin polarization and anisotropy of symmetry-broken phases.
Theoretical Modeling: Self-consistent Hartree-Fock calculations were performed to simulate the competition between Hund's coupling and spin-orbit coupling, predicting ground state phases and canting angles.

Key Results

Emergence of New Superconducting Pockets: In WSe $_2$ -supported RTG, two new superconducting pockets (SC1 for hole doping and SC2 for electron doping) appear when carriers are polarized adjacent to the WSe $_2$ layer. The maximum $T_c$ for SC1 reaches $\approx 300$ mK, approximately three times higher than in "bare" RTG (hBN-encapsulated only). No superconductivity is observed in the weak-SOC quadrants ( $n_e \cdot D < 0$ ).
Spin-Canting Transition: Magnetometry and compressibility data reveal that superconductivity straddles a transition between a spin-canted state (with a finite in-plane magnetic moment) and a spin-valley-locked state (with complete spin-valley locking, $\phi = 0$ $ϕ = 0$ ).
- In bare RTG, magnetic phases are dominated by ferromagnetic Hund's coupling, resulting in fully spin-polarized states.
- In WSe $_2$ -proximitized RTG, the competition between SOC and carrier-density-tuned Hund's interaction leads to a continuous transition where the canting angle $\phi$ evolves from $90^\circ$ (fully polarized) to $0^\circ$ (spin-valley locked).
Nature of the Transition: The transition between the spin-canted and spin-valley-locked phases appears continuous, consistent with Hartree-Fock simulations. The in-plane spin moment $\langle s_\parallel \rangle$ and the energy difference between phases evolve smoothly to zero at the transition.
Superconductivity and Canting Angle: The superconducting state (specifically SC1) is observed to emerge from a regime with finite in-plane spin moments ( $0 < \phi < 90^\circ$ ). At the low- $|D|$ boundary of the superconducting pocket, the system transitions to a spin-valley-locked state ( $\phi \approx 0$ ), where superconductivity is suppressed. The domain of superconductivity expands with in-plane magnetic fields, suggesting the competing normal state possesses a finite in-plane moment.

Significance and Claims
The paper argues that the enhancement of superconductivity by spin-orbit coupling is not driven by a change in the fundamental ground state symmetry or degeneracy, but rather by a quantitative change in the spin-canting angle.

The results support a mechanism where superconductivity is mediated by fluctuations in the spin-canting order. The authors note that superconductivity appears only when the system hosts both large and small Fermi pockets (disjoint topology) and when the canting angle is non-zero but less than $90^\circ$ . This aligns with theoretical predictions (Ref. [15]) suggesting that scattering between these pockets, driven by spin-canting fluctuations, contributes to the pairing interaction. The study establishes that the nucleation of high- $T_c$ superconducting pockets via SOC proximity is a generic feature of rhombohedral graphene multilayers and highlights the critical role of the interplay between Hund's coupling and SOC in tuning the pairing strength.

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