Systems with strong spin-orbit coupling, which competes with other interactions and energy scales, offer a fertile playground to explore new correlated phases of matter. Weyl semimetals are an example where the phenomenon leads to a low-energy effective theory in terms of massless linearly dispersing fermions in three dimensions. In the absence of interactions chirality is a conserved quantum number, protecting the semimetallic physics against perturbations that are translationally invariant. In this Letter we show that the interplay between interaction and topology yields a novel chiral excitonic insulator. The state is characterized by a complex vectorial order parameter leading to a gapping out of the Weyl nodes. A striking feature is that it is ferromagnetic, with the phase of the order parameter determining the direction of the induced magnetic moment.

• Received 20 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.196403