🔬 mesoscale physics

Dirac charge in antiferromagnetic topological semimetals

This study reveals that antiferromagnetic Dirac semimetals possess a hidden "Dirac charge" acting as a source or sink of Berry curvature in a generalized parameter space, which can be experimentally detected through spin-charge-coupled photocurrent responses.

Original authors: Kohei Hattori, Hikaru Watanabe, Ryotaro Arita

Published 2026-02-02

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CC0 1.0

Original authors: Kohei Hattori, Hikaru Watanabe, Ryotaro Arita

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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 city made of tiny, invisible roads where electrons (the city's travelers) move. In most materials, these roads are smooth and predictable. But in special materials called topological semimetals, the roads twist and turn in ways that create "traffic hubs" or nodes.

This paper explores a specific type of these materials called Antiferromagnetic (AFM) Dirac Semimetals. Here's the story of what the researchers found, explained simply:

1. The Mystery of the "Hidden Charge"

In some of these special materials (called Weyl semimetals), the traffic hubs act like lighthouses. They emit a kind of invisible "magnetic wind" (called Berry curvature) that pushes electrons in a specific direction. Scientists call this a "Weyl charge," and it's easy to spot because it creates a strong, measurable current when you shine light on the material.

However, in Dirac semimetals, things are trickier. Because the electrons have a property called "spin" (think of it as a tiny internal compass pointing up or down), the traffic hubs come in pairs. One pushes the wind one way, and its partner pushes it the other way. They cancel each other out, making the "charge" invisible. For a long time, scientists thought these Dirac points were just neutral, boring spots with no hidden power.

2. The New Discovery: The "Spin-Charge" Connection

The researchers in this paper realized that while the electric winds cancel out, there is a hidden layer of complexity involving the spins of the electrons and the spins of the atoms in the material.

They discovered a new kind of "charge" hidden inside these Dirac points, which they call the "Dirac charge."

The Analogy: Imagine the traffic hub isn't just a signpost, but a spinning top. Even if the top's movement doesn't push the cars (electrons) forward directly, it creates a swirling wind in the air around it (the "mixed parameter space").
This "Dirac charge" acts as a source or sink for this swirling wind, but only if you look at the relationship between the electron's movement and its spin.

3. How They "Saw" the Invisible

Since this charge is hidden, you can't see it with a normal flashlight. The researchers needed a special tool to detect it: Spin-Charge Coupled Motive Force.

The Metaphor: Imagine trying to push a heavy cart (the electron) that is stuck. If you just push it (using electricity), it might not move because of the cancellation effect. But, if you also wiggle the handle of the cart (shaking the local spins of the atoms) while pushing, the cart suddenly starts rolling.
In the experiment, they used light to make the atoms' spins wiggle (dynamics) while applying an electric field. This combination created a "motive force" that unlocked the hidden Dirac charge.

4. The Result: A New Kind of Current

When they applied this special "wiggle-and-push" method, they measured a photocurrent (a flow of electricity generated by light).

The Finding: The strength of this current wasn't random. It spiked dramatically when the energy of the light matched the specific energy levels of the Dirac points.
The Proof: These spikes in the current were the "fingerprint" of the Dirac charge. The researchers used computer simulations (real-time modeling) to confirm that without this hidden charge, the current would be much weaker. The charge was the main engine driving the current in these specific conditions.

Summary

In simple terms, this paper says:

Dirac points in certain magnetic materials were thought to be "invisible" because their effects canceled out.
The researchers found a hidden "Dirac charge" that exists in the relationship between electron movement and spin.
By using light to make the material's internal spins wiggle, they could detect this hidden charge as a surge of electricity.
This proves that even when things look balanced and neutral, there can be powerful, hidden topological forces at play that can be unlocked with the right combination of light and spin dynamics.

The paper concludes that this discovery opens a door to understanding the "hidden properties" of these materials, which could be useful for future technologies that rely on controlling electron spins (spintronics), though the paper focuses strictly on the physics of detection rather than specific future gadgets.

Technical Summary: Dirac Charge in Antiferromagnetic Topological Semimetals

Problem Statement
Topological semimetals are characterized by linear electronic dispersion around degenerate points (nodes). In Weyl semimetals, these nodes carry a "Weyl charge," acting as sources or sinks of Berry curvature in momentum space, which leads to quantized injection currents under circularly polarized light. However, in Dirac semimetals, the presence of spin degeneracy typically compensates for the Berry curvature monopole, rendering the emergent charge of the Dirac point elusive. While photocurrent generation driven by order parameter dynamics (such as localized spin dynamics) has been observed in various systems, the specific role of topological features in antiferromagnetic (AFM) Dirac semimetals remains unclear. This study addresses the existence of a hidden "Dirac charge" in AFM Dirac semimetals and investigates its detectability via photocurrent responses driven by spin-charge coupling.

Methodology
The authors employ a combination of analytical derivations within an effective Dirac Hamiltonian framework and real-time numerical simulations.

Theoretical Framework:
- Generalized Parameter Space: The study introduces Berry curvature (BC) defined in a generalized parameter space $R = (k, S)$ , where $k$ is the wave vector and $S$ represents the localized spin configuration. Three types of BC are considered: momentum-space BC ( $\Omega_{kk}$ ), spin Berry curvature ( $\Omega_{SS}$ ), and mixed Berry curvature ( $\Omega_{kS}$ ).
- Model Hamiltonian: A two-dimensional AFM Dirac semimetal model is constructed, including an electronic Hamiltonian with staggered spin-orbit coupling, an exchange interaction term between electronic and localized spins, and a magnetic anisotropy term to stabilize collinear AFM order (analogous to CuMnAs).
- Effective Hamiltonian: An effective Dirac Hamiltonian is derived around the Dirac points ( $D_1, D_2$ ) to analytically calculate the BC components.
- Photocurrent Formalism: The injection current conductivity is formulated using perturbation theory, linking the current to the quantum geometry (Berry connection and curvature) driven by external electric fields and light-driven localized spin dynamics.
Numerical Simulation:
- Real-Time Dynamics: The authors solve the coupled von Neumann equation (for the single-particle density matrix of the electronic system) and the Landau-Lifshitz-Gilbert (LLG) equation (for the localized spin dynamics).
- Decomposition: The total photocurrent is decomposed into three components: the electric field effect, the interference between spin dynamics and the electric field, and the pure localized spin dynamics contribution.

Key Contributions and Results

Definition of Dirac Charge: The study identifies the Dirac point as a "Dirac charge," acting as a source or sink for the mixed Berry curvature ( $\Omega_{kS}$ ) and spin Berry curvature ( $\Omega_{SS}$ ) in the generalized parameter space. Analytical expressions show that these curvatures behave as vector fields scaling as $\rho/|\rho|^3$ (where $\rho$ is a generalized momentum vector), analogous to the classical field of a point charge.
Detection Mechanism: The authors demonstrate that the Dirac charge can be detected via the injection current driven by a spin-charge-coupled motive force. Specifically, the injection current conductivity reflects the source or sink nature of the quantum geometry around the Dirac nodes.
Role of Energy Splitting: In AFM Dirac semimetals, two Dirac nodes exist with opposite Dirac charges. While their contributions to the photocurrent might cancel, the energy difference ( $2\Delta$ ) between the nodes prevents complete cancellation due to Pauli blocking. This results in a net, detectable photocurrent.
Analytical and Numerical Verification:
- Analytical calculations of the injection current conductivity reveal a "flat-topped" peak structure centered at the chemical potentials corresponding to the Dirac points ( $\pm \Delta$ ). The magnitude of these peaks directly reflects the defined Dirac charge.
- Real-time simulations of the Kondo lattice Hamiltonian confirm these findings. The simulations show that the photocurrent components driven by spin-charge coupling ( $\sigma_{col-E}$ and $\sigma_{col-col}$ ) exhibit broad peaks around the Dirac point energies.
- Crucially, the contribution from the Dirac charge is found to be comparable in magnitude to the photocurrent generated by the direct electric field effect, indicating its significant role in the total photocurrent generation, particularly in broadband filling regimes.

Significance
The paper claims to reveal a hidden property of Dirac points in AFM Dirac semimetals: the existence of a Dirac charge that acts as a source/sink for mixed and spin Berry curvatures. By linking this topological feature to the injection current driven by spin-charge coupling, the work provides a theoretical mechanism for detecting this charge experimentally. The authors suggest that this phenomenon is relevant for electrically switchable AFM Dirac semimetals (e.g., CuMnAs) and note that the concept of Dirac charge could be extended to other Fermion-Boson coupled systems, such as electron-phonon coupling systems. The work bridges the gap between order parameter dynamics and topological band properties, offering a new perspective on transport phenomena in antiferromagnetic topological materials.