| Weyl fermions | |
|---|---|
| Name | Weyl fermion |
| Composition | Elementary (theoretical) |
| Statistics | Fermi–Dirac |
| Spin | 1/2 |
| Discovered | 1929 (theoretical), 2015 (condensed matter quasiparticles) |
| Discoverer | Hermann Weyl |
Weyl fermions
Weyl fermions are massless chiral fermions described by the Weyl equation, a two-component form of the Dirac equation introduced by Hermann Weyl in 1929. They play a central conceptual role in relativistic quantum field theory and in modern condensed matter physics as emergent quasiparticles in Weyl semimetals; their chiral nature underpins anomalous transport and topological responses relevant to both high-energy and materials physics.
Weyl fermions were proposed by Hermann Weyl as solutions of a massless form of the relativistic wave equation that carry definite chirality (left-handed or right-handed). Early work on chiral spinors influenced the development of quantum electrodynamics and later the Standard Model of particle physics, where chirality is a fundamental ingredient in the electroweak interaction. Although no elementary massless charged Weyl fermion has been conclusively observed in particle accelerators, theoretical interest persisted because of their connection to chiral anomalies and symmetry structure in theories studied by researchers at institutions such as CERN and the Institute for Advanced Study. In condensed matter, predictions by Haldane, Volovik, and others laid groundwork; experimental discovery of Weyl quasiparticles in materials such as TaAs and NbAs was reported in 2015 by groups including those led by Ashvin Vishwanath and collaborators, using techniques developed at facilities like the Advanced Light Source.
Weyl fermions are described by the Weyl equation, a two-component spinor equation obtained by imposing the massless limit on the four-component Dirac spinor. The Weyl Hamiltonian has the linear form H = ±v_F σ·p, where σ are the Pauli matrices and the sign labels chirality. Weyl spinors transform under the (1/2,0) or (0,1/2) representations of the Lorentz group and are eigenstates of the chirality (γ^5) operator in the massless limit. Their dispersion relation is linear (E = ±v_F |p|), implying relativistic-like kinematics and a vanishing rest mass. In gauge theories, coupling of Weyl fermions to gauge fields leads to subtle quantum effects such as the chiral anomaly and potential violation of classical current conservation at the quantum level; consistent gauge theories must arrange chiral fermions to cancel gauge anomalies, as in the Standard Model anomaly cancellation conditions.
In high-energy theory, Weyl fermions are the building blocks for chiral theories: the left-handed and right-handed components of a Dirac fermion are Weyl spinors. The electroweak interaction couples differently to chiral components, making Weyl fermions central to gauge theory model building and grand unified theories studied at places like SLAC National Accelerator Laboratory and Fermilab. Theoretical developments such as the Atiyah–Singer index theorem and the understanding of anomalies by Adler, Bell, and Jackiw hinge on properties of Weyl fermions. Proposed extensions of the Standard Model sometimes include massless Weyl fermions or nearly massless chiral states; searches for sterile or chiral neutrinos touch on this topic in neutrino experiments like DUNE and Super-Kamiokande.
In crystals, low-energy band crossings with nondegenerate linear dispersion act as Weyl nodes, realized in Weyl semimetals. Such materials break either time-reversal symmetry or inversion symmetry to separate Weyl nodes in momentum space; canonical examples include the transition-metal monopnictides TaAs and NbAs and magnetic compounds studied at Max Planck Institute for Chemical Physics of Solids. Each Weyl node acts as a monopole of Berry curvature characterized by an integer topological charge (Chern number). The existence of Fermi arc surface states connecting projections of Weyl nodes on crystal surfaces is a hallmark experimental signature predicted by topological band theory and observed by angle-resolved photoemission spectroscopy (ARPES) experiments.
Key experimental probes include ARPES for band structure and Fermi arcs, quantum oscillation measurements (Shubnikov–de Haas and de Haas–van Alphen) for bulk topology, and transport experiments revealing anomalous Hall and negative longitudinal magnetoresistance attributed to the chiral anomaly. Synchrotron facilities such as the Advanced Photon Source and research groups at Lawrence Berkeley National Laboratory have produced high-resolution ARPES maps of Weyl materials. Scanning tunneling microscopy (STM) and optical spectroscopy also probe surface and bulk electronic structure. Careful analysis is required to separate extrinsic effects (disorder, conventional magnetoresistance) from intrinsic Weyl physics.
Weyl fermions realize the chiral anomaly in condensed matter: applying parallel electric and magnetic fields pumps charge between nodes of opposite chirality, producing a negative longitudinal magnetoresistance and nonconservation of chiral charge in effective field theories. Berry curvature acts as a magnetic field in momentum space, giving anomalous velocity terms responsible for the intrinsic anomalous Hall effect. Topological invariants (monopole charges of Weyl nodes) protect nodes against weak perturbations; however, pairs of nodes of opposite chirality can annihilate when brought together, allowing topological phase transitions. The interplay of topology and interactions has been studied using techniques from topological band theory and many-body quantum field theory.
Active research includes engineering Weyl physics in heterostructures, photonic and acoustic analogues, and cold-atom simulators; exploring effects of strong electron correlations and superconductivity proximate to Weyl nodes; realizing non-Abelian or interacting chiral states; and searching for elementary Weyl fermions or related chiral particles in high-energy experiments. Theoretical work addresses disorder and localization in Weyl systems, interaction-driven instabilities, and lattice regularization of chiral fermions (overlaps with lattice gauge theory). Cross-disciplinary efforts at universities and national labs aim to exploit Weyl transport for devices and to deepen understanding of topology in quantum matter.
Category:Quantum field theory Category:Condensed matter physics Category:Topological phases of matter