🔬 mesoscale physics

Optical conductivity signature of Van Hove singularity in altermagnetic topological systems

This paper demonstrates that optical and magneto-optical spectroscopy can serve as sensitive probes for detecting altermagnet-induced Van Hove singularities and Dirac gaps in two-dimensional $d$ -wave altermagnetic topological systems, characterized by distinct signatures in joint density of states, optical conductivities, and Faraday/Kerr rotations.

Original authors: Fang Qin, Rui Chen, Xiao-Bin Qiang

Published 2026-08-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Fang Qin, Rui Chen, Xiao-Bin Qiang

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

In the vast landscape of materials science, researchers are constantly searching for substances that can manipulate the flow of electricity in new and useful ways. For decades, the focus has been on magnets that pull in one direction or materials where electrons move without resistance. Recently, however, a new class of magnetic materials has emerged, known as altermagnets. These are unique because, unlike traditional magnets that have a strong overall pull, altermagnets have a net magnetization of zero. Yet, inside the material, the electrons still behave as if they are strongly polarized, splitting their paths based on their spin. This hidden order creates a complex internal landscape where electrons can travel in specific, anisotropic ways. Scientists are eager to understand how these materials interact with light, as shining a beam on them could reveal their secret internal structures and potential uses in future electronics.

A team of researchers has now mapped out exactly how light interacts with a specific type of these altermagnetic materials, revealing a clear optical fingerprint of a phenomenon known as a Van Hove singularity. In the world of solid-state physics, a Van Hove singularity is a point in the energy landscape of a material where the available states for electrons to occupy suddenly pile up, much like cars slowing to a crawl at a bottleneck on a highway. This congestion creates a distinct peak in the material's response to energy. The researchers focused on a two-dimensional model of a d-wave altermagnet, a theoretical system that combines the unique spin-splitting of altermagnets with the effects of spin-orbit coupling and an external magnetic field. By simulating how this system responds to light, they discovered that the material's optical conductivity—the measure of how easily it conducts electricity when hit by light—carries a direct signature of these singularities.

The study began by constructing a mathematical model of the material's electronic structure. The system was designed to have specific high-symmetry points where the energy bands of electrons meet and open up into gaps, known as Dirac gaps. The researchers calculated the joint density of states, which essentially counts how many electron-hole pairs can be created when a photon of a certain energy strikes the material. They found that as the energy of the incoming light increased, the number of available transitions jumped sharply at the frequencies corresponding to the Dirac gaps. More importantly, at a specific frequency determined by the material's internal parameters, the joint density of states spiked into a pronounced peak. This peak corresponds exactly to the Van Hove singularity, where the electrons' group velocity drops to zero, causing them to crowd together in energy space.

What makes this discovery particularly significant is how the altermagnetic order influences these optical signals. The researchers compared the behavior of the material when the d-wave altermagnetic term was active against a scenario where it was absent. When the altermagnetic order was present, the peak associated with the Van Hove singularity appeared clearly in the transverse optical conductivity, which measures how the material responds to light in a direction perpendicular to the electric field. However, when the altermagnetic term was removed, this specific peak in the transverse conductivity vanished. This result demonstrates that the Van Hove singularity leaves a unique optical fingerprint that is induced specifically by the altermagnetic order. Without that specific magnetic arrangement, the signature disappears, proving that the effect is not just a generic feature of the material but a direct consequence of its altermagnetic nature.

The team also explored how these optical properties translate into magneto-optical effects, specifically the Faraday and Kerr rotations. These are phenomena where the plane of polarization of light rotates as it passes through or reflects off a magnetic material. The simulations showed that the Faraday and Kerr angles inherited the characteristic features of the optical conductivity. The frequency dependence of the Faraday rotation closely mirrored the real part of the transverse conductivity, while the Kerr rotation followed the imaginary part. This means that by simply measuring how the light rotates as it interacts with the material, scientists could detect the presence of the Van Hove singularity and the specific altermagnetic order without needing to probe the material's internal structure directly.

The findings suggest that optical and magneto-optical spectroscopy can serve as highly sensitive tools for probing these complex topological systems. The researchers showed that the positions of the Dirac gaps and the Van Hove singularities are not fixed; they can be tuned by adjusting the strength of the altermagnetic order, the spin-orbit coupling, and the Zeeman splitting. This tunability implies that the optical signatures are dynamic and can be manipulated. The study establishes a clear link between the microscopic arrangement of electrons in altermagnets and the macroscopic way they interact with light. By identifying these specific spectral features, the work provides a roadmap for experimentalists to identify and characterize altermagnetic topological phases in real materials, potentially opening the door to new types of spintronic devices that rely on these unique magnetic properties.

Problem Statement
While recent advances have identified altermagnets as a new class of magnetic materials featuring momentum-space spin splitting without net magnetization, the optical signatures associated with Van Hove singularities in these systems remain largely unexplored. Specifically, the interplay between altermagnetic order, spin-orbit coupling (SOC), and Zeeman splitting in determining the Van Hove singularity features within the optical conductivity of altermagnetic topological systems has not been clarified. Previous studies have addressed magneto-optical conductivity in the presence of Landau levels or substrate-induced SOC, but a detailed investigation into how d-wave altermagnetism specifically modulates the optical response near Van Hove singularities is lacking.

Methodology
The authors investigate a two-dimensional tight-binding model of a d-wave altermagnet incorporating Rashba spin-orbit coupling and a Zeeman splitting term. The Hamiltonian includes three components: SOC, the d-wave altermagnetic order (which breaks time-reversal symmetry while preserving combined $C_{4z}T$ symmetry), and a Zeeman term arising from exchange interactions.

Topological Analysis: The authors analytically derive the conditions for energy gap closing at high-symmetry points ( $\Gamma, M, X, Y$ ) and calculate the Chern number of the valence band using the Berry curvature to map the topological phase diagram.
Joint Density of States (JDOS): The JDOS is calculated to characterize available interband transitions, identifying characteristic frequencies associated with Dirac gaps and Van Hove singularities.
Optical Conductivity: Using the Kubo formula at zero temperature, the authors compute the longitudinal ( $\sigma_{xx}$ ) and transverse ( $\sigma_{xy}$ ) optical conductivities.
Magneto-Optical Effects: The Faraday and Kerr rotation angles are derived from the optical conductivity tensors to simulate experimental observables for normally incident light.

Key Results

Band Structure and Topology: The system hosts Dirac gaps at the high-symmetry points $\Gamma, M, X,$ and $Y$ . The gap sizes are tunable by the altermagnetic order ( $t_J$ ) and Zeeman splitting ( $\Delta_z$ ). The system exhibits topological phases with Chern numbers $C = \pm 1$ and a trivial phase ( $C=0$ ), depending on the ratio of $t_J$ to $\Delta_z$ .
JDOS Signatures: The JDOS displays kinks at frequencies corresponding to the Dirac gaps. Crucially, it exhibits pronounced peaks at Van Hove singularities. The positions of these singularities are explicitly tunable by varying the altermagnetic order, SOC strength, and Zeeman splitting.
Optical Conductivity:
- Longitudinal ( $\sigma_{xx}$ ): The real part shows an abrupt onset at the threshold frequency ( $\omega_0$ ) and a pronounced peak at the Van Hove frequency ( $\omega_V$ ). For finite $t_J$ , additional features (drops and peaks) appear at frequencies $\omega_X$ and $\omega_Y$ due to the lifting of equivalence between high-symmetry points.
- Transverse ( $\sigma_{xy}$ ): In the topologically nontrivial regime ( $t_J \neq 0$ ), the zero-frequency conductivity is quantized. The real part exhibits a pronounced dip at the Van Hove frequency ( $\omega_V$ ).
Altermagnet-Induced Fingerprint: A central finding is that the distinct Van Hove signatures in the transverse optical conductivity (specifically the dip at $\omega_V$ ) disappear entirely when the d-wave altermagnetic term is absent ( $t_J = 0$ ). This reveals that the Van Hove signature in the transverse channel is an optical fingerprint induced specifically by the d-wave altermagnetism.
Magneto-Optical Rotations: The Faraday and Kerr rotation angles inherit the characteristic frequency dependencies of the optical conductivity. The Faraday angle closely tracks the real part of the transverse conductivity, while the Kerr angle follows the imaginary part, providing experimentally accessible probes of the underlying electronic structure.

Significance and Claims
The paper establishes optical and magneto-optical spectroscopy as sensitive probes for detecting Dirac gaps and Van Hove singularities in altermagnetic topological systems. The authors claim that their results provide a method to extract information about altermagnetic order and band topology through the observation of specific spectral features. Most notably, the work demonstrates that the presence of Van Hove signatures in the transverse optical conductivity serves as a direct indicator of d-wave altermagnetism, distinguishing it from systems with only SOC and Zeeman splitting. These findings offer a theoretical framework for identifying and characterizing altermagnetic materials and their topological phases via spectroscopic measurements.

More like this