Dirac and Weyl Fermions: The Revolutionary Particles Powering Tomorrow's Technology
Exploring the exotic particles hidden in topological semimetals that could transform electronics, quantum computing, and energy technologies
The Universe in a Crystal
Imagine holding a piece of crystal in your hand that contains within it the same exotic particles that physicists believe played a fundamental role in the birth of our universe.
These aren't ordinary particles; they are Weyl and Dirac fermions—elusive entities that once were thought to exist only in the realm of quantum physics and cosmic phenomena, yet have now been found hiding within the atomic lattice of certain remarkable materials known as topological semimetals.
Scientific Breakthrough
The discovery marks the convergence of abstract mathematical concepts, quantum theory, and materials science.
Technological Potential
From electronics with minimal energy loss to quantum computers leveraging exotic particle behaviors.
The Particles That Shouldn't Be There
From Quantum Theory to Condensed Matter
To appreciate the significance of Weyl and Dirac fermions in topological semimetals, we must first understand their origins in theoretical physics. In the 1920s, physicist Hermann Weyl made a startling prediction: the existence of a massless, chiral fermion that would come to bear his name 1 .
The revolutionary insight came when scientists realized that these exotic particles could emerge as low-energy excitations within certain crystalline materials 1 . In this context, they're not fundamental particles but quasiparticles—collective excitations of electrons that behave as if they were these long-sought particles.
Key Scientists
Hermann Weyl
Predicted Weyl fermions in 1929Paul Dirac
Dirac equation (1928)Modern Researchers
Experimental discovery in 2015Dirac vs. Weyl: A Matter of Chirality
The distinction between Dirac and Weyl fermions lies in a property called chirality, or "handedness." Think of chirality like your hands—mirror images that cannot be perfectly superimposed onto one another.
Dirac fermions can be thought of as combining two Weyl fermions of opposite chirality.
- Combine two Weyl fermions
- No definite chirality
- Found in Dirac semimetals
When separated in momentum space within a material, these give rise to Weyl fermions with definite chirality—either left-handed or right-handed 1 .
- Definite chirality
- Come in pairs of opposite chirality
- Found in Weyl semimetals
Visualizing Weyl Nodes and Fermi Arcs
In Weyl semimetals, these chiral fermions appear at points where the conduction and valence bands touch, known as Weyl nodes 6 . These nodes always come in pairs of opposite chirality and are remarkably stable—they can't be removed without the two partners of opposite chirality meeting and annihilating each other.
The topological nature of these materials gives rise to their most striking feature: Fermi arcs. Unlike ordinary metals where the Fermi surface forms closed loops, Weyl semimetals can host open arcs on their surfaces that connect the projections of the Weyl nodes 1 .
Catching Weyl Fermions in the Wild
The Tantalum Arsenide Breakthrough
For years, Weyl fermions remained a theoretical prediction in condensed matter physics. That changed in July 2015 when two independent research groups made a landmark discovery. Through a combination of theoretical prediction and experimental ingenuity, they identified the first topological Weyl fermion semimetal in single-crystal tantalum arsenide (TaAs) 1 .
Crystal Growth
Researchers first needed to create high-quality TaAs single crystals large enough to study. This was achieved using the chemical vapor transport method with iodine as a transport agent, producing crystals of approximately 1 cm in size 1 .
Surface Preparation
The crystals were carefully cleaved in vacuum to expose pristine surfaces for measurement. Different crystal facets—{001}, {101}, and {112}—were examined to fully map the electronic structure 1 .
ARPES Measurements
Scientists directed ultraviolet or X-ray light onto the crystal surfaces and measured the kinetic energy and emission angles of the ejected electrons. By collecting millions of these data points, they could reconstruct the electronic band structure.
Data Analysis
The resulting data was analyzed to identify the characteristic signatures of Weyl fermions: the linear dispersion (indicating massless behavior) and the presence of Fermi arcs on the surface connecting Weyl nodes of opposite chirality.
Properties of Tantalum Arsenide (TaAs)
| Property | Description | Significance |
|---|---|---|
| Crystal Structure | Body-centered tetragonal | Lack of inversion symmetry enables Weyl state |
| Space Group | I41md (No. 109) | Essential symmetry for Weyl fermion realization |
| Lattice Constants | a = 3.44 Å, c = 11.64 Å | Determines electronic band structure |
| Key Experimental Method | Angle-resolved photoemission spectroscopy (ARPES) | Directly images electronic structure and Fermi arcs |
| Topological Signature | Surface Fermi arcs | Proof of nontrivial topology |
Experimental Triumph
The ARPES measurements revealed exactly what the theorists had predicted: clear signatures of Weyl points in the bulk electronic structure and the corresponding Fermi arcs on the surface 1 .
"You can keep peeling the surface of TaAs, but the arcs are always there."
A New Frontier: Higher-Order Topology and Dirac Semimetals
Beyond Surface States: The Discovery of Hinge Fermi Arcs
Just as scientists were digesting the implications of Weyl semimetals, another surprise emerged from theoretical and experimental work on their close cousins—Dirac semimetals. In 2020, an international team of researchers discovered that Dirac semimetals exhibit an even more exotic form of topological behavior called higher-order topology 2 .
While Weyl semimetals host topological states on their surfaces (Fermi arcs), higher-order topological Dirac semimetals exhibit conducting electronic states in just one dimension—or two fewer dimensions than the bulk 3D material. These hinge Fermi arcs (HOFAs) appear along the edges where two surfaces meet, like the hinges of a box 2 5 .
Higher-Order Topology
Topological states exist in dimensions lower than the surface—at the hinges or corners of a material.
Research Tools for Studying Topological Semimetals
| Tool/Material | Function/Role | Examples |
|---|---|---|
| Angle-Resolved Photoemission Spectroscopy (ARPES) | Directly images electronic band structure and surface states | Used to discover Fermi arcs in TaAs 1 |
| Chemical Vapor Transport | Grows high-quality single crystals for study | Used to create cm-sized TaAs crystals 1 |
| Magneto-optical Spectroscopy | Probes electronic response to magnetic fields from THz to visible range | Used in DIRAC3D project to study Landau level lasers 3 |
| Ab Initio Calculations | Computes electronic structure from first principles | Predicted hinge states in Cd₃As₂ 2 |
| Dirac Semimetal Materials | Platforms for studying massless Dirac fermions | Cd₃As₂, Na₃Bi, KMgBi 2 5 |
| Weyl Semimetal Materials | Host Weyl fermions with topological surface states | TaAs, WTe₂, MoTe₂ 1 |
"Unlike Weyl semimetals, whose surface states are cousins of the surfaces of topological insulators, we have shown that Dirac semimetals can host surface states that are cousins of the corner states of higher-order topological insulators."
From Laboratory Curiosity to Revolutionary Technology
Electronics and Computing
The high mobility of Weyl fermions arises from their topological protection—they can travel through the material without being easily scattered by impurities or defects 1 .
This property could lead to ultra-low power electronic devices that generate less heat and operate more efficiently than conventional semiconductors.
Energy Applications
In 2019, researchers discovered that the Weyl semimetal Tantalum Arsenide delivers the largest intrinsic conversion of light to electricity of any material 1 .
This suggests potential for highly efficient solar energy conversion and photodetection technologies.
Quantum Computing
Nanorods of higher-order topological semimetals could realize topological superconductivity on their surfaces when combined with conventional superconductors.
This could potentially create Majorana fermions for fault-tolerant quantum computers 2 .
Recent Advances and Future Prospects
The field of topological semimetals continues to evolve rapidly. Recent research has uncovered:
Application Potential of Topological Semimetals
| Application Area | Potential Benefit | Current Status |
|---|---|---|
| Low-Power Electronics | High electron mobility reduces energy loss | Experimental demonstration in TaAs 1 |
| Quantum Computing | Potential platform for Majorana fermions | Theoretical prediction 2 |
| Photovoltaics | Enhanced light-to-electricity conversion | Observed in TaAs 1 |
| Terahertz Sources | Active medium for Landau level lasers | Demonstrated in DIRAC3D project 3 |
| Thermoelectric Devices | Giant Nernst effect for cooling applications | Observed in TaSb₂ 7 |
| Spintronics | Spin-polarized currents for information processing | Demonstrated in 2D Weyl semimetals 1 |
Technology Readiness Level of Topological Semimetal Applications
The Future is Topological
The discovery of Dirac and Weyl fermions in topological semimetals represents one of the most exciting developments in condensed matter physics this century.
What began as a theoretical curiosity has blossomed into a rich field bridging abstract mathematics, quantum field theory, and materials science. These materials provide us with a unique laboratory for studying phenomena that were previously only accessible to high-energy physicists, while simultaneously offering tremendous potential for technological innovation.
Research Trajectory
As research continues, we're likely to see even more exotic topological phases and unexpected applications emerge.
- Higher-order topology discoveries
- Weyl ferromagnets with unique properties
- Enhanced thermoelectric effects
- New materials with tailored topological states
Material Diversity
The family of topological semimetals continues to expand with new materials exhibiting unique properties.
Fundamental Research Drives Innovation
The journey of topological semimetals—from mathematical abstraction to laboratory reality—serves as a powerful reminder that fundamental curiosity-driven research often lays the foundation for tomorrow's technological revolutions.
As we continue to explore the topological universe hidden within crystals, we may well be witnessing the birth of a new technological paradigm based on the intricate geometry of the quantum world.