Axion electrodynamics and giant magnetic birefringence in Weyl excitonic insulators

We study the electromagnetic (EM) response of the excitonic insulator phase of a time-reversal (TR) invariant Weyl semimetal (WSM). At low temperatures, the system develops two exciton condensates. The condensates are related to each other by TR symmetry and weakly coupled by a Josephson tunneling term. The latter leads to the formation of the Leggett mode with a small gap. Our main finding is that the Leggett mode couples to the EM fields as a massive dynamical axion. This is a consequence of the chiral anomaly and the chiral magnetic effect in the parent WSM. Due to the small axion mass, its coupling to EM fields results in a giant anisotropic polarizability and birefringence in the presence of a static magnetic field. The photon-axion hybridization produces a polariton resonance near the axion gap.