Weyl fermion

Weyl fermion. In particle physics and condensed matter physics, a Weyl fermion is a massless, chiral elementary particle proposed as a building block for other fermions. It is a solution to the Dirac equation that was first theorized by the mathematician Hermann Weyl in 1929. While long sought as a fundamental particle in high-energy physics, its clearest experimental realizations have been as emergent quasiparticle excitations in certain exotic materials, fundamentally changing the understanding of electronic behavior in solids.

Definition and mathematical description

The concept originates from the work of Hermann Weyl, who sought solutions to the relativistic wave equation formulated by Paul Dirac. A Weyl fermion is described by the Weyl equation, a simplified form of the Dirac equation that governs massless particles with a definite chirality, being either purely left-handed or right-handed. This mathematical description implies that its spin is locked parallel or anti-parallel to its direction of motion, a property known as helicity. The theoretical framework for these particles is deeply connected to concepts in quantum field theory and the representation theory of the Poincaré group. Their existence is also intimately tied to the physics of neutrinos, which were once thought to be potential candidates for such massless, chiral particles before the discovery of neutrino oscillation.

Discovery and experimental evidence

For decades, searches in facilities like the Large Hadron Collider at CERN failed to identify Weyl fermions as fundamental particles. A major breakthrough occurred in 2015 when several independent research teams provided the first solid experimental evidence for Weyl fermions as quasiparticles in synthetic crystals. One key study, published in *Science*, involved researchers from Princeton University and collaborators analyzing the semimetal tantalum arsenide. Concurrently, a group at the Massachusetts Institute of Technology reported similar findings in niobium phosphide. These discoveries were made using advanced techniques like angle-resolved photoemission spectroscopy at facilities such as the Advanced Light Source to directly observe the characteristic Weyl points in the electronic band structure.

Physical properties and behavior

As massless particles, Weyl fermions travel at an effective speed analogous to the speed of light within their host material. Their most distinctive property is the chiral anomaly, a quantum phenomenon where the number of particles of a given chirality is not conserved in the presence of parallel electric and magnetic fields, leading to novel transport signatures. This results in unusual effects like the negative magnetoresistance observed in experiments. Furthermore, their band structure features topologically protected Weyl points where valence and conduction bands touch, acting as sources and sinks of Berry curvature. This structure gives rise to exotic surface states known as Fermi arcs, which connect the projections of these Weyl points on the material's surface.

Role in condensed matter physics

The realization of Weyl fermions in materials has established the new class of topological materials known as Weyl semimetals. These materials, including compounds like tantalum arsenide and cadmium arsenide, exhibit extraordinarily high electron mobility and are predicted to host other unusual phenomena. Research led by institutions like the Chinese Academy of Sciences and the Max Planck Institute explores their potential for low-power electronics and spintronics due to their dissipationless chiral currents. The study of these systems bridges condensed matter physics with ideas from high-energy physics, providing a tangible laboratory for testing quantum field theory effects that are otherwise inaccessible.

Theoretical significance in particle physics

In the Standard Model of particle physics, all known fermions, such as quarks and leptons, acquire mass through the Higgs mechanism and are therefore not fundamental Weyl fermions. However, the theory is fundamentally chiral, with left-handed and right-handed components transforming differently under the weak interaction, governed by the gauge theory of the Standard Model. The mathematical structure of Weyl spinors is essential for formulating theories like the see-saw mechanism, which explains the small masses of neutrinos. Furthermore, Weyl fermions are central to several beyond-Standard Model theories, including some versions of supersymmetry, and their properties are crucial for understanding potential violations of CP symmetry in the early universe.

Category:Elementary particles Category:Condensed matter physics Category:Quasiparticles