| Weyl fermion | |
|---|---|
| Name | Weyl fermion |
| Composition | Elementary (hypothetical) / quasiparticle (condensed matter) |
| Statistics | Fermionic |
| Spin | 1/2 |
| Charge | 0 (originally massless neutral); can appear with charge in solids |
| Discovered | 1929 (theoretical: Hermann Weyl) / 2015 (condensed matter experiments) |
| Group | Lorentz group |
Weyl fermion
Weyl fermions are massless spin‑1/2 particles described by the Weyl equation and characterized by definite chirality. They were first proposed theoretically by Hermann Weyl in 1929 as solutions to relativistic wave equations; although no fundamental Weyl fermion was confirmed in high‑energy particle accelerators as of the late 2010s, Weyl fermions have become central to modern condensed matter physics as low‑energy quasiparticles in Weyl semimetals. Their study links concepts in quantum field theory, topology, and materials science.
A Weyl fermion is a massless fermionic excitation whose wavefunction transforms as a two‑component spinor under the Lorentz group. Hermann Weyl introduced two‑component spinors as an alternative formulation of the Dirac equation in 1929. The early history intersects with work by Paul Dirac and later with the understanding of parity violation in weak interactions by T. D. Lee and C. N. Yang and the discovery of the neutrino's chiral behavior. Interest resurged when condensed matter theorists predicted quasiparticle realizations in crystals, leading to experimental reports by groups at institutions such as Princeton University and Paul Scherrer Institute in the 2010s.
Mathematically, a Weyl fermion is represented by a two‑component complex spinor Ψ that satisfies the Weyl equation. The representation belongs to the (1/2,0) or (0,1/2) irreducible representations of the SL(2,C) spin group, corresponding to left‑handed or right‑handed chirality. Key properties include linear dispersion (E = ±c|p| in particle physics) and the absence of a Lorentz‑invariant mass term that couples left and right components. In quantum field theory, Weyl fields are used to build Majorana spinors and Dirac spinors; anomaly structure, such as the chiral anomaly, is computed from Weyl contributions. Group‑theoretic classification also relates Weyl fermions to representations of Poincaré group and to topological invariants in momentum space.
The Weyl equation is the two‑component relativistic wave equation obtained by decoupling the Dirac equation into chiral sectors. It can be written using Pauli matrices σ^μ and a two‑spinor ψ as σ^μ ∂_μ ψ = 0 (natural units). Solutions have definite chirality, meaning eigenstates of the chirality operator γ^5 (in four‑component language) or helicity in the massless limit. Chirality and helicity coincide for strictly massless particles, which yields robust symmetry constraints: Weyl fermions violate parity when appearing alone, and their coupling structure under gauge symmetry can produce gauge anomalies unless appropriately canceled by other species, as in the Standard Model anomaly cancellation conditions.
In high‑energy theory, Weyl fermions are fundamental building blocks of chiral gauge theories: the left‑handed and right‑handed components in the Standard Model are Weyl fields. The theoretical possibility of truly massless charged Weyl fermions is constrained by empirical searches and anomaly cancellation. Weyl fermions play a central role in discussions of the chiral anomaly, axial anomaly, and related processes such as anomalous current nonconservation in electromagnetic and gauge backgrounds. Extensions of particle physics, including grand unified theories (e.g., SU(5) models) and supersymmetry, routinely use Weyl spinor notation for fermionic degrees of freedom.
Condensed matter systems realize Weyl fermions as emergent low‑energy quasiparticles near band‑crossing points (Weyl points) in the electronic band structure of certain crystals. Weyl semimetals, predicted theoretically by groups including Xiao‑Liang Qi and Ashvin Vishwanath and realized in materials such as TaAs and NbAs, host pairs of Weyl points with opposite chirality. These points act as monopoles of Berry curvature in momentum space, characterized by Chern numbers. The topology enforces surface states known as Fermi arcs connecting projections of bulk Weyl points on the Brillouin zone boundary. Materials realization connects to techniques and institutions like angle‑resolved photoemission spectroscopy (ARPES) at facilities such as SLAC National Accelerator Laboratory and synchrotrons.
Signatures of Weyl fermions in solids include ARPES observation of Fermi arcs, anomalous magnetotransport such as the chiral magnetic effect and negative longitudinal magnetoresistance, and optical responses tied to Berry curvature. Experiments reported evidence in transition‑metal monopnictides (e.g., TaAs) through combined ARPES and transport studies by groups at universities like Stanford University and laboratories including Paul Scherrer Institute. Quantum oscillation measurements, scanning tunneling microscopy (STM), and magneto‑optical probes complement spectroscopic results. In particle physics, searches for elementary Weyl fermions overlap with neutrino experiments (e.g., Super‑Kamiokande) and collider constraints from CERN.
Weyl fermions inform theory across multiple domains: they exemplify chiral quantum field theories, underpin anomaly inflow and topological classifications, and motivate concepts like axial gauge fields and emergent relativistic symmetry in lattice systems. Extensions include interacting Weyl liquids, superconducting states hosting Majorana modes derived from paired Weyl fermions, and engineered platforms such as photonic and cold‑atom Weyl points. The interplay with topology has driven connections to the Atiyah–Singer index theorem and modern classification schemes (K‑theory). Weyl fermions thus remain a focal point linking mathematical physics, materials discovery, and fundamental particle theory.
Category:Quantum field theory Category:Condensed matter physics Category:Elementary particles