Weyl and Dirac semimetals in three-dimensional solids

TLDR

Weyl and Dirac semimetals are three‑dimensional phases with gapless, topologically protected excitations, analogous to graphene, and exhibit protected surface states and unique electromagnetic responses. This review seeks to survey the theoretical foundations, proposed solid‑state realizations, recent experimental observations, and relationships of Weyl and Dirac semimetals to other topological phases. The authors compile and analyze theoretical models, experimental data, and comparative studies of candidate materials to elucidate the properties and potential applications of these semimetals.

Abstract

Weyl and Dirac semimetals are three dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and -- despite their gaplessness -- to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. Here we review the theoretical foundations of these phases, their proposed realizations in solid state systems, recent experiments on candidate materials, as well as their relation to other states of matter.