Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves

Abstract

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Letter, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion- ($\mathcal{I}$-) symmetric Weyl-CDWs with $\varphi =0,\pi$ differ by a topological axion angle $\delta {\theta }_{\varphi }=\pi$. However, we crucially discover that $neither$ of the minimal Weyl-CDW phases at $\varphi =0,\pi$ is individually an AXI; they are instead quantum anomalous Hall (QAH) and "obstructed" QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. 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, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings, and provide models and analysis generalizing our results to nonmagnetic Weyl- and Dirac-CDWs.

arXiv commentv3: approximately published verison. v2: Fixed typos, clarified discussion of applicability to real material systems, and added extensions to time-reversal invariant models. 4.5 + 11pgs + references, 4+3 figures. v1: 4.5 + 7pgs + references, 4+1 figures

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