Weylsemimetals

Weyl semimetals are three-dimensional crystalline solids in which the valence and conduction bands intersect at isolated points, known as Weyl nodes, in momentum space. Near each node the electronic states are described by the Weyl equation, yielding massless Weyl fermions. Each node carries a chirality, +1 or −1, and nodes appear in pairs of opposite chirality. In a lattice this pairing arises when either time-reversal or inversion symmetry is broken.

Topologically, Weyl nodes act as monopole sources of Berry curvature. Their chiral charges are conserved. The bulk topology enforces surface states called Fermi arcs, which connect the projections of Weyl nodes of opposite chirality on the surface Brillouin zone. The nodes can be separated in momentum or energy depending on the broken symmetry; the conical dispersion tilt distinguishes type-I from type-II.

Several materials have been identified as Weyl semimetals, notably the TaAs family (TaAs, TaP, NbAs, NbP), with experimental demonstrations around 2015 imaging Weyl nodes and Fermi arcs. Experimental signatures include angle-resolved photoemission spectroscopy imaging and transport measurements showing chiral-anomaly effects. Type-I Weyl semimetals host upright cones, while type-II exhibit strongly tilted cones producing electron and hole pockets; examples of type-II materials include MoTe2 and WTe2.

Weyl semimetals are of interest for fundamental studies of topology in solids and may enable novel electronic, spintronic, and optoelectronic devices. Their low-energy excitations and surface states offer platforms for exploring Berry curvature effects and chiral anomaly phenomena, contributing to ongoing efforts to map material realizations and understand their potential applications in quantum materials research.