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, electronlike and holelike 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 ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, 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.

Figure 1

Left: Fermi-arc metal states at fixed low energy in mixed momentum real space $(k_x,k_y,z)$ shown as position of the wave function centers $z_{\mathit{k}n\chi }$ (red/blue helical lines for chirality $\chi =+/-$). Right: Same states but in the all-momentum space $(k_x,k_y,k_z)$, where they form nested cylindrical electronlike and holelike Fermi surfaces for chirality $+$ and $-$, respectively. Both figures illustrate excitonic pairing of two states (red/blue spheres) of opposite chirality at the Fermi surface, whih are at the same momentum (right) but separated in $z$ by $\pi /Q$ (left), which protects them from single-particle hybridization.