# Weyl and Dirac Semimetals in Three Dimensional Solids

## TL;DR

This paper reviews Weyl and Dirac semimetals, three-dimensional topological phases with gapless excitations, discussing their theoretical basis, experimental realizations, and unique electronic properties in solid-state systems.

## Contribution

It provides a comprehensive overview of the theoretical foundations, experimental progress, and connections of Weyl and Dirac semimetals to other topological phases.

## Key findings

- Identification of candidate materials for Weyl and Dirac semimetals
- Observation of protected surface states in experiments
- Unique electromagnetic responses of these materials

## 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.