Axionic band topology in inversion-symmetric Weyl-charge-density waves

In this talk, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW systems. We show that, as a function of the CDW phase, the system transitions between two distinct inversion-symmetric topological phases, differing by a pi shift in the electromagnetic theta angle. Crucially, low-energy critical theory for the transition is that of an axion insulator (AXI), neither phase is itself AXI. Using symmetry indicators of band topology and non-abelian Berry phase, we demonstrate that our results generalize to multi-band systems with only two Weyl fermions, and explore the consequences for transport measurements. We extend our results to time-reversal invariant Weyl or Dirac-CDWs, showing that the CDW phase in these systems mediates a helical higher-order topological phase transition. We conclude with a discussion of the experimental implications of our findings.