page_title: Weyl semimetal
hierarchical_section_title: Weyl semimetal
caption_attribution_description: English: A Schematic of the Weyl semimetal state, which include the Weyl nodes and the Fermi arcs. The Weyl nodes are momentum space monopoles and anti-monopoles.
context_page_description: Weyl fermions are massless chiral fermions embodying the mathematical concept of a Weyl spinor. Weyl spinors in turn play an important role in quantum field theory and the Standard Model, where they are a building block for fermions in quantum field theory. Weyl spinors are a solution to the Dirac equation derived by Hermann Weyl, called the Weyl equation. For example, one-half of a charged Dirac fermion of a definite chirality is a Weyl fermion.
  Weyl fermions may be realized as emergent quasiparticles in a low-energy condensed matter system. This prediction was first proposed by Conyers Herring in the context of electronic band structures of solid state systems such as electronic crystals. Topological materials in the vicinity of band inversion transition became a primary target in search of topologically protected bulk electronic band crossings.
  The first liquid state which is suggested has similarly emergent but neutral excitation and theoretically interpreted superfluid's chiral anomaly as observation of Fermi points is in Helium-3 A liquids.
context_section_description: Weyl fermions are massless chiral fermions embodying the mathematical concept of a Weyl spinor.  Weyl spinors in turn play an important role in quantum field theory and the Standard Model, where they are a building block for fermions in quantum field theory. Weyl spinors are a solution to the Dirac equation derived by Hermann Weyl, called the Weyl equation. For example, one-half of a charged Dirac fermion of a definite chirality is a Weyl fermion.
  Weyl fermions may be realized as emergent quasiparticles in a low-energy condensed matter system. This prediction was first proposed by Conyers Herring in the context of electronic band structures of solid state systems such as electronic crystals. Topological materials in the vicinity of band inversion transition became a primary target in search of topologically protected bulk electronic band crossings. 
  The first (non-electronic) liquid state which is suggested has similarly emergent but neutral excitation and theoretically interpreted  superfluid's chiral anomaly as observation of Fermi points is in Helium-3 A liquids. Crystalline tantalum arsenide (TaAs) is the first discovered topological Weyl fermion semimetal exhibiting topological surface Fermi arcs where Weyl fermion is electrically charged along the line of original suggestion by Herring. An electronic Weyl fermion is not only charged but stable at room temperature where there is no such superfluid or liquid state known.
caption: A schematic of the Weyl semimetal state, which include the Weyl nodes and the Fermi arcs. The Weyl nodes are momentum space monopoles and anti-monopoles. The sketch is adapted from Ref.[9]
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