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Ising Dirac fermions across a topological phase transition

This study reports the emergence of six-fold degenerate Dirac fermions in twisted WSe₂ moiré systems across a quantum spin Hall transition, demonstrating a new route to realizing Dirac physics in strongly spin–orbit-coupled materials and establishing a platform for high-mobility spintronics.

Original authors: Kaifei Kang, Aoqian Zhang, Yaqi Ma, Yifei Jin, Nan Zhang, Wentao Jiang, Tianyu Qiao, Ivana Wong, Ulf Lampe, Kenji Watanabe, Takashi Taniguchi, Tze Kin Cheung, Junwei Liu, Shilin Huang, Xi Dai, Hoi Chu

Published 2026-07-15

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Kaifei Kang, Aoqian Zhang, Yaqi Ma, Yifei Jin, Nan Zhang, Wentao Jiang, Tianyu Qiao, Ivana Wong, Ulf Lampe, Kenji Watanabe, Takashi Taniguchi, Tze Kin Cheung, Junwei Liu, Shilin Huang, Xi Dai, Hoi Chun Po, Ning Wang

Original paper licensed under CC BY 4.0 (https://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 tiny, flat world made of two sheets of a special material called WSe₂, stacked on top of each other but twisted slightly, like two pancakes that aren't perfectly aligned. In this twisted sandwich, electrons don't just sit still; they zoom around, and usually, when they hit a certain speed or angle, they get stuck in a "traffic jam" called an energy gap. This usually stops them from flowing freely.

But here's the magic trick the researchers discovered: by twisting the sheets at just the right angle (about 3.65 degrees) and applying a specific electric push, they found a way to make the traffic jam disappear completely. Instead of getting stuck, the electrons started behaving like Dirac fermions.

Think of Dirac fermions as super-fast, ghost-like runners who don't feel any weight. In most materials, these runners are heavy and slow down because of a force called "spin-orbit coupling" (which is like a strong wind pushing them off course). Usually, this wind is so strong that it forces the runners to stop and sit down (becoming an insulator). However, in this twisted WSe₂ sandwich, the researchers found a special "sweet spot" right at the boundary between two different states of matter. Here, the energy gap that usually traps the runners closes up, allowing them to become light and fast again, creating a Dirac semimetal.

The Six-Fold Mystery
The most exciting part is how these runners organize themselves. The team measured how the electrons moved under a magnetic field and saw a very specific pattern, like a fan opening up.

On one side (where there are extra "holes" in the electron crowd), the runners grouped themselves in sixes. It's as if they were dancing in groups of six, perfectly synchronized.
On the other side (where there are extra electrons), they danced in pairs.

This "six-fold" grouping is a huge deal because it proves these aren't just ordinary electrons; they are these special, massless Dirac particles that the team calls "Ising Dirac fermions." The "Ising" part just means they are locked into spinning in a specific direction, like a top that can only spin up or down, never sideways.

The Magic Angle and the Switch
The researchers didn't just find this by accident; they mapped out a whole landscape. They discovered that if you twist the angle too little (under 3.3 degrees), the electrons get stuck in a "Quantum Spin Hall" state, which is like a highway where cars can only drive on the very edge of the road, never in the middle.

But if you twist it just a tiny bit more (above 3.3 degrees), the highway opens up in the middle, turning the whole road into a smooth, fast lane for these Dirac runners. They found that this fast lane exists over a wide range of electric fields, not just at one tiny, fragile point. It's like finding a wide, open valley between two mountains, rather than a narrow, precarious bridge.

What They Ruled Out
The paper is very clear about what this is not. It's not a case where the electrons are just moving slowly or getting stuck in a normal metal state. The measurements showed that the resistance (how hard it is for the electrons to move) dropped to a very low, specific value, and the electrons didn't act like a normal metal that gets colder and more conductive as it cools down. Instead, they showed a "weakly metallic" behavior that fits perfectly with the theory of these special Dirac particles.

How Sure Are They?
The team is very confident in what they saw. They didn't just guess or run a computer simulation; they built real devices, cooled them down to 1.5 Kelvin (which is colder than outer space), and measured the electricity flowing through them with extreme precision. They saw the same patterns in multiple devices and with different twist angles. They measured the "Landau fan" (the pattern of electron groups under a magnetic field) and saw the exact half-integer steps that only Dirac fermions can make.

So, in simple terms: The team twisted a special material just right, turned on an electric switch, and watched as heavy, stuck electrons suddenly turned into light, fast, six-dancing ghosts. They proved that even in materials where these ghosts are usually banned, you can create a whole new world for them to play in, right at the edge of a topological phase transition.

Technical Summary: Ising Dirac Fermions Across a Topological Phase Transition

Problem Statement
Dirac fermions, characterized by linearly dispersing energy bands and a $\pi$ Berry phase, are central to topological physics. While spin-isotropic Dirac fermions are well-established in systems like graphene, their realization in two-dimensional systems with strong Ising spin–orbit coupling (SOC) presents a significant challenge. In such systems, strong SOC typically opens a mass gap at Dirac points, driving the material into either a trivial or topological insulating state. Although theoretical proposals suggest Dirac fermions could survive under specific nonsymmorphic symmetries or fine-tuned conditions, experimental realizations of robust Dirac quasiparticles in strongly spin–orbit-coupled materials remain elusive. Furthermore, while topological phase transitions (TPTs) offer a route to gap closing and band crossing, stabilizing these Dirac states over a finite parameter range rather than a single critical point is a major experimental hurdle.

Methodology
The authors investigate twisted bilayer WSe $_2$ (tWSe $_2$ ), a moiré system where strong Ising SOC locks spins to the out-of-plane direction, creating spin–valley-locked states. The study employs a quad-gate device architecture fabricated via tear-and-stack and dry transfer techniques, utilizing hexagonal boron nitride (hBN) encapsulation and graphite gates to independently control carrier density (via a vertical electric field, $E$ ) and twist angle ( $\theta$ ).

The experimental approach involves:

Electrical Transport Characterization: Measuring longitudinal resistance ( $R_{xx}$ ) and nonlocal resistance ( $R_{nl}$ ) across a range of moiré filling factors ( $\nu$ ) and vertical electric fields at low temperatures (1.4–24 K).
Magnetotransport Analysis: Applying out-of-plane magnetic fields ( $B$ ) up to 14 T to map Landau level (LL) formation and extract degeneracy factors using the Středa formula.
Parameter Space Mapping: Systematically varying the twist angle ( $\theta$ ) from 2.29° to 3.89° to construct a phase diagram distinguishing between Quantum Spin Hall (QSH) and Dirac semimetal regimes.

Key Results

Emergence of Ising Dirac Fermions: In a device with a twist angle of $\theta \approx 3.65^\circ$ , the authors observe a distinct phase transition. At high electric fields ( $|E| > 0.3$ V/nm), the system exhibits a QSH phase with nearly quantized resistance ( $R_{xx} \approx h/2e^2$ ) and pronounced nonlocal signals. Conversely, near zero electric field ( $|E| < 0.3$ V/nm), the system enters a Dirac semimetal phase characterized by low resistance ( $< 2$ k $\Omega$ ) and bulk-dominated transport.
Landau Fan Quantization: Magnetotransport measurements in the Dirac phase reveal a half-integer Landau fan sequence, a hallmark of Dirac fermions with a $\pi$ $π$ Berry phase.
- Hole-doped side ( $\nu < -2$ ): The Landau levels exhibit a six-fold degeneracy, following the sequence $N = -3, -6, -9, \dots$ (where $N$ is the level index).
- Electron-doped side ( $\nu > -2$ ): The levels show a two-fold degeneracy, following the sequence $N = 1, 3, 5, \dots$ .
- This particle-hole asymmetry is attributed to band-structure asymmetry and velocity renormalization in the moiré bands.
Temperature Dependence: The Dirac semimetal phase displays weak metallic behavior, with resistance decreasing only slightly upon cooling from 24 K to 1.4 K. In contrast, the QSH phase shows insulating behavior (resistance increasing by an order of magnitude upon cooling), and the trivial metallic phase shows strong metallic temperature dependence.
Phase Diagram and Critical Twist Angle: By varying the twist angle, the authors identify a critical angle $\theta_c \approx 3.3^\circ$ $θ_{c} \approx 3. 3^{\circ}$ .
- For $\theta < 3.3^\circ$ , the system remains in the QSH phase across the entire electric field range.
- For $\theta > 3.3^\circ$ , a finite electric field window opens where the Dirac semimetal phase exists, bounded by a critical displacement field $E_c$ that increases linearly with the twist angle.

Significance and Claims
The paper claims to report the experimental realization of six-fold degenerate Dirac fermions in an Ising spin–orbit-coupled system, emerging specifically across a quantum spin Hall phase transition. The primary significance lies in demonstrating that Dirac fermions can persist despite strong Ising SOC, challenging the expectation that such interactions invariably gap out Dirac points.

The authors posit that the stability of the Dirac phase over a finite parameter range (rather than a single critical point) is enabled by the broken inversion symmetry in the monolayer WSe $_2$ triangular lattice and its moiré superlattice. They suggest that the Dirac points are protected by specific symmetries ( $C_{2x}$ and $C_{2z}$ ) that allow the gap to close over an extended region of momentum space.

The work establishes twisted transition metal dichalcogenides (TMDs) as a versatile platform for exploring:

Spin-polarized Dirac physics: Unlike graphene, these states are intrinsically spin–valley locked and strongly spin-polarized.
Topological phase transitions: Providing a controllable route to access relativistic quasiparticles at the boundary between topological and trivial insulating states.
High-mobility spintronics: The observation of Dirac fermions in a moiré system with strong SOC offers a promising pathway for developing spintronic functionalities.

The authors remain modest regarding the specific mechanisms of symmetry breaking on the electron side, noting that the reduced degeneracy likely reflects spontaneous symmetry breaking or band asymmetry, but they emphasize the robustness of the observed half-integer quantization as a definitive signature of the Ising Dirac nature of the quasiparticles.

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