Axionic Instability of Periodic Weyl-Semimetal Superstructures

Weyl-semimetal superstructures with a spiraling position of a pair of Weyl nodes of opposite chirality can host a chiral-symmetry preserving Fermi-arc metal state, where the chirality is carried by cylindrical Fermi surfaces, electron- and hole-like depending on the chirality. The Fermi surfaces nest at vanishing momentum separation (zero nesting vector) at the electron-hole-compensation energy because the nesting is topologically protected by vanishing spatial overlap of any pair of equal-momentum opposite-chirality states. In this work we show that the nesting and Coulomb interaction drive a spontaneous chiral symmetry breaking in such a Fermi arc metal, which leads to a dynamical axion insulator state but without breaking translational symmetry (no charge-density-wave order) as in a conventional Weyl semimetal. As for material realization, we discuss magnetically doped Bi$_2$Se$_3$, for which the Weyl-node positions depend on the order of the magnetic dopands. In this case, the axionic condensation can itself stabilize a spiral order of the magnetization, and hence the spiraling node positions, even if the magnetic interaction is intrinsically ferromagnetic.