Nonlinear axion dynamics in topological Weyl semimetal*

The concept of Weyl fermions was first hypothesized in the context of high energy physics to describe massless chiral fermions, but has since been applied to describe quasiparticle excitations in condensed matter materials with topologically-enforced band-crossings. These particles naturally have an additional chiral symmetry which enriches transport, e.g. presence of Fermi arcs. However, the chiral anomaly serves to break this symmetry, which leads to a static axion response, characterized by topological magnetoelectric effects such as the chiral magnetic effect or anomalous Hall effect.

The situation becomes more complex when chiral symmetry is spontaneously broken by the introduction of charge density wave (CDW) order. The Goldstone mode of the CDW then acts as a dynamical axion mode, and may possess a signature in e.g. negative longitudinal magnetoresistance. However, to date identifying this collective mode has posed a serious experimental and theoretical challenge.  Therefore, we present a new route towards detecting the axion mode based on a nonlinear optical response of the magnetoelectric interaction. We propose signatures based on the frequency and polarization dependence in these spectroscopies which can conclusively identify this elusive collective mode. Finally, various material candidates and signatures are considered, as well as possible complications and constraints.