Functional Dirac Materials: Status and Perspectives

The Rise of a New Electronic Frontier

In the world of materials science, a revolutionary class of substances is redefining the boundaries of physics and engineering.

Explore the Science

Known as Dirac materials, these compounds exhibit a peculiar and extraordinary property: their electrons behave as if they have no mass, moving at incredible speeds while barely scattering. This phenomenon, which mirrors the physics of cosmic particles, is not happening in a distant galaxy, but in laboratories working with ultra-thin, two-dimensional materials. The study of these materials has coalesced into a vibrant field of research, leading to a 2018 workshop by NORDITA that summarized the status and future perspectives of what are now termed "Functional Dirac Materials"—systems where these unique electronic properties can be harnessed for practical applications 1 .

From faster electronics to the robust protection of quantum information, the potential of these materials is vast. This article explores the captivating science behind Dirac materials, highlights a groundbreaking recent experiment, and examines the tools that are pushing this frontier forward.

The Essence of Dirac Materials: Massless Electrons and Conical Energy Landscapes

What makes these materials so special is their unique electronic band structure that enables electrons to behave as if they have no mass.

What Makes a Material "Dirac"?

At the heart of every material is its band structure—a map of how the energy of electrons relates to their momentum. In most conventional materials like silicon, this relationship is parabolic; much like a thrown ball, the energy of an electron increases with the square of its momentum. Dirac materials are different. They are characterized by a linear band dispersion, meaning the energy of their electrons increases in a straight line with momentum 8 .

This linear relationship is described by the Dirac cone, a conical energy-momentum structure where the energy of electrons goes to zero at the tip of the cone, the Dirac point 9 .

Remarkable Properties

Extremely High Mobility

Charge carriers in Dirac materials can move with exceptionally high speeds and little resistance 8 .

Nodal Points

The Dirac point is where the valence and conduction bands meet, leading to a change in conductive behavior 8 .

Topological Protection

Conductive surface states are protected against scattering by time-reversal symmetry 1 .

A Diverse Family Tree

The family of Dirac materials is surprisingly diverse, encompassing several well-known and exotic members:

Graphene

A single layer of carbon atoms arranged in a honeycomb lattice 4 .

Topological Insulators

Like Bi₂Se₃, insulating in bulk but hosting conducting surface states 1 .

3D Dirac Semimetals

Like cadmium arsenide, exhibiting Dirac points in three dimensions 1 .

Novel 2D Materials

Hf₂S₂ and Re₂S₂ predicted to exhibit Dirac points .

A Deep Dive into a Key Experiment: The Hunt for Dirac Exceptional Points

A landmark 2025 experiment achieved the first-ever observation of a hybrid quantum state known as a Dirac exceptional point 6 .

Background: Exceptional Points

Exceptional Points (EPs) are exotic degeneracies that occur in non-Hermitian systems—systems that are not energy-conserving, often due to energy gain or loss. For over half a century, only two types of EPs were known. The 2025 experiment successfully observed a theorized third type: the Dirac Exceptional Point, which merges the concepts of Dirac points from Hermitian systems and EPs from non-Hermitian systems 6 .

Methodology: Engineering a Hybrid Quantum State

Researchers from the University of Science and Technology of China engineered this novel state using a sophisticated step-by-step approach 6 :

System Selection

The experiment was performed on nitrogen-vacancy (NV) centers in diamond. These are atomic-scale defects in a diamond's crystal lattice that act as highly controllable quantum systems.

Hamiltonian Engineering

The team designed a specific non-Hermitian Hamiltonian predicted to host Dirac EPs. A key step was introducing a spin-squared operator term (Sₚ²) into a three-level quantum system.

Experimental Implementation

Using a previously developed method called the dilation technique, the researchers implemented this custom-tailored Hamiltonian in the solid-state environment of the diamond NV center.

Measurement and Confirmation

The existence of the Dirac EP was confirmed by measuring two key signatures: the observation of real eigenvalues near the EP and a clear eigenstate degeneracy at the EP itself.

Results and Analysis: Defying Conventional Wisdom

Overcoming Dissipation

Conventional EPs are always accompanied by complex eigenvalues, which represent energy loss or gain and prevent stable quantum evolution. The Dirac EP, however, exhibits a real-valued energy spectrum in its vicinity 6 . This challenges the traditional understanding of non-Hermitian physics and suggests a path to achieve stable, adiabatic evolution even in dissipative systems.

Path to Quantum Control

The ability to avoid the non-adiabatic transitions associated with typical EPs makes Dirac EPs a promising platform for developing high-fidelity quantum control protocols and for studying complex geometric phases in open quantum systems 6 . This has implications for the development of more robust quantum sensors and computers.

Comparison of Dirac Point and Dirac Exceptional Point

Feature Dirac Point Dirac Exceptional Point
System Type Hermitian (energy-conserving) Non-Hermitian (with gain/loss)
Core Feature Linear Dirac cone dispersion Degeneracy blending Dirac point and Exceptional Point
Eigenvalues Always real Real in the vicinity of the EP
Key Significance Massless Dirac fermions, high electron mobility Enables adiabatic evolution in dissipative systems
Primary Application Potential High-speed electronics Topological quantum control, robust quantum sensing

The Expanding Universe of Dirac Materials

The discovery of new Dirac materials is a rapidly advancing frontier. First-principles calculations have been instrumental in predicting novel two-dimensional structures that host Dirac physics.

Properties of Selected Novel 2D Dirac Materials

Material Dirac Point Location Key Characteristic SOC-Induced Bandgap
Hf₂S₂ Along high-symmetry path Highly anisotropic Dirac cone; Fermi velocity comparable to graphene 37.21 meV
Re₂S₂ K-point in the Brillouin zone Transitions to an antiferromagnetic (AFM) state with Hubbard U correction; exhibits valley polarization 253.49 meV
Hf₂S₂ Applications

Hf₂S₂'s anisotropic Dirac cone suggests potential for direction-dependent electronic devices, where current flows much more easily in one direction than another .

Re₂S₂ Applications

Re₂S₂'s emergence as a Dirac-Mott insulator with intralayer antiferromagnetic properties makes it a promising candidate for spintronics and quantum computing applications, where its magnetic and valley properties could be used to encode information .

Spintronics Potential
Quantum Computing
Valleytronics

The Scientist's Toolkit: Key Resources in Dirac Material Research

The exploration and application of Dirac materials rely on a sophisticated array of theoretical and experimental tools.

Generalized Dirac Hamiltonian

Low-energy effective model describing electron dynamics in the material 2 8 .

Theoretical
Green's Function Methods

Analytical calculation of quantum transport, accounting for edges and interfaces 8 .

Computational
Density Functional Theory (DFT)

First-principles computational method to predict electronic structure .

Computational
Nitrogen-Vacancy (NV) Centers

Atomic-scale, solid-state platform for quantum engineering and simulation 6 .

Experimental
Electric Field Gating

External control parameter to tune material properties like Fermi velocity 9 .

Experimental
Advanced Microscopy

STM, ARPES, and TEM for direct visualization of Dirac cone structures.

Characterization

Essential Tools for Dirac Material Research

Tool / Resource Primary Function Example in Use
Generalized Dirac Hamiltonian Low-energy effective model describing electron dynamics in the material 2 8 Used to derive band structure and predict quantum transport properties.
Green's Function Methods Analytical calculation of quantum transport, accounting for edges and interfaces 8 Computing density of states and scattering probabilities in germanene.
Density Functional Theory (DFT) First-principles computational method to predict electronic structure Predicting stability and Dirac points in novel materials like Hf₂S₂ and Re₂S₂.
Nitrogen-Vacancy (NV) Centers Atomic-scale, solid-state platform for quantum engineering and simulation 6 Used to experimentally realize and probe non-Hermitian Hamiltonians with Dirac EPs.
Electric Field Gating External control parameter to tune material properties like Fermi velocity 9 Fine-tuning the slope of the Dirac cone in a topological insulator junction.

Conclusion & Future Perspectives

The journey into the world of functional Dirac materials is just beginning.

The 2018 NORDITA workshop highlighted ongoing challenges and vibrant research directions, including understanding the interplay between bulk and interface properties, exploring dynamic quantum matter, and even leveraging these materials for novel applications like dark matter detection 1 .

The future of this field lies in the continued synergy between theory, computation, and experiment. As researchers develop new methods to fabricate high-quality materials and devise more sophisticated theoretical models, the path will open for transformative technologies.

Potential Applications of Dirac Materials

High-Speed Electronics

Electronic devices with unprecedented speed and efficiency enabled by massless Dirac fermions.

Quantum Computing

Quantum computers that leverage topological protection for fault-tolerant operation.

Advanced Sensors

Sensors of extraordinary sensitivity for medical, environmental, and security applications.

The exploration of Dirac materials is not merely about understanding a new state of matter—it is about actively constructing the technological landscape of tomorrow.

For the foundational review discussed in this article, please see: Functional Dirac Materials: Status and Perspectives 3

References